Imagine a world much like our own. Exactly like our own, in fact, at first glance! Burger Kings are prevalent, Nic Cage is the greatest actor known to mankind, and groups of teenagers still spend nearly all their time talking to each other with instant messaging clients. Now take that world and make it infinitely more complicated and strange and you have the Homestuck world!
One of the many strange things about this world is the prevalence of mechanics that would usually be only present in video games. Things such as the inventory system they use, in which they can place any physical object into a card which is stored in a Sylladex, are considered completely normal. The same goes for their assigning weapons to a Strife specubus, allowing them to keep weapons of that type in a card as well. These things are apparently entirely accepted as normal, to the point that John and Jade both received various additions to them for holidays. It's a weird damn world!
This version of Earth, as well, possesses an entity known as the First Guardian, which mostly guides the world towards creating a new universe via the game of Sburb. The First Guardian of this specific Earth is a large dog named Becquerel, who protects Jade as her pet slash guardian. This is very important for Jadesprite.
The third of these many complications is, of course, the fact that the entirety of Earth was ravaged by meteors, due to the playing of a game called Sburb by four children. Sburb is a "video game" of (mostly) unknown origins. Its purpose, or "winning condition", is to create a new universe- any universe that has Sburb in it is doomed from the start, and the only way to create a new universe for the lucky few who play is to complete the game, defeating the dark army of Derse and create a new universe. The universe the kids live in- our universe- was created by a group of twelve Trolls, an alien race from Alternia who played their own version of the game, known as "Sgrub". Their victory created our own universe, but due to a slip-up later made by Jade (which only happened due to a slip-up by Karkat, one of the trolls), they were unable to claim it as their own, and remained in their own desolate, dead game session.
When playing Sburb, or a variation, a certain "entry ritual" is required to transport the player from their world, which is bombarded with meteors from the moment the first player installs the game, to the game session. One of the items necessary to enter the game creates an energy being known as a Kernelsprite; the first form it takes is that of a glowing ball of energy, laced with the symbol of Skaia. It is intended that the player should combine the kernel with an item of emotional value, usually something or someone who is dying or near-death; this process, known as Prototyping, imbues the Kernelsprite with attributes and powers of the item chosen. Upon entering the game, or by prototyping a second item, the Kernelsprite splits into two- the Kernal, or a sheer manifestation of the items prototyped, which powers up the rings of the monarchs of Skaia, and the Sprite itself, which retains the personality, memories, and powers of the item chosen. Jade's sprite, of course, combined Becquerel, the First Guardian (as well as her pet dog), and her then-deceased dreamself, creating Jadesprite.
As for the four kids playing Sburb- John, Rose, Dave, and Jade- they have been tied into in the game from long before they were born. This accounts for several oddities in their lives, although not all of them are aware of it until they enter the Incipisphere, the mini solar system that the game transports them to, and that most of the gameplay takes place in. The Incipisphere contains Prospit and Derse, the players' Lands, and the Battlefield. For instance, the four children of Homestuck have guardians that are not related to them in a normal fashion. Instead, the kids and guardians were all ectocloned from time-imprints of themselves, a process done by one of the kids (John), creating a bizarre self-sustaining time loop. In short, the kids and their guardians would literally have never existed if they did not participate in Sburb.
Another oddity: the kids are provided with a dreamself from birth, a perfect physical copy of themselves that lives on the moons of Prospit and Derse. This dreamself is usually asleep and inactive, and can be woken by any number of methods (from having a new understanding of themselves like a literalized 'awakening', to simply being slapped). When the dreamself is awake, the kid will be able to use it like an extra body: As their waking self sleeps, their consciousness moves over to their dreamself, and vice versa. The dreamself is not precisely the same person as their waking-self, given that they have lived all their life on a moon overlooking an alien city; in Jade's case, her dreamself (who has been awake for most of her life) tends to be a little sillier and less-focused than she is when she's awake. The waking self remembers things from their dreams, but they are very fuzzy, as if they happened a long time ago, or, of course, in a dream; the opposite apparently applies to the dreamselves with the memories of their waking selves.
Aside from allowing the kids to play the game while getting some shut-eye, a dreamself also acts as an extra life, just like a 1-UP in a video game. If the kids' original body is killed, their consciousness will permanently move to their dream-self and they can continue as normal. More than that, though, is how it ties in with the concept of god tiers. God tiers are basically the bonus final 100* level that a Sburb player can reach, and requires a player to be killed on a special Quest Bed, while both their real- and dreamselves are alive, in a sort of sacrifice to themselves. When this happens, the player's consciousness moves to their dreamself, which undergoes a transformation. They get an Important Costume Change, an immense boost in ability, and nigh-immortality (the only way they can die is if it's in a heroic or just fashion, like in a suicidal rescue attempt or being taken down after going muahahaha-evil).
When a dreamself dies first, however, things change a bit. When falling a sleep, the player still takes control of their dreamself; however, since they are dead, they instead awake in the afterlife, a series of bubbles on the edge of the universe known as Dreambubbles. (If both the dreamself and the normal self die, this is also where a fully dead player ends up, without the temporary escape of waking up.) Within these bubbles, reality's laws don't apply; it's possible to relive the past, or the present, to visit others who have died, and to hear the great Horrorterrors, the dark gods living at the edges of the Incipisphere. When a dreambubble bursts the afterlife becomes nothing but a terrifying (for most people- Feferi seems to enjoy it) experience of hearing the whispers of the gods directly in your mind, without the protective bubble of the afterlife to muffle them. Jadesprite dwelled in these bubbles for a very, very long time, and being removed from them to come back to life was jarring, at the least.
Jadesprite, is, well. A crybaby! This is basically the absolute first word that would come to mind when describing her, because other than the dog thing- which isn't really describable in one word- the first thing most people would notice is that she's almost constantly sobbing about one thing or another. She's incredibly fatalistic, assumes she's going to fail at everything, and tends to assume that other people do things around or to her just to make her life harder. Compounding this further is the fact that when she starts crying, she's nearly impossible to stop, regardless of the methods taken to comfort her- in fact, she's occasionally continued crying to the point where all that that's achieved is making the other person cry too.
Jadesprite's depression primarily stems from an intense inferiority complex, as well as her jarring creation. While in the afterlife she was always worried she'd failed John, she was still very content to be amongst her friends from Prospit, a happy and relatively worry-free afterlife. And then, suddenly, she was dragged back to life, in a strange place, with the Green Sun constantly burning in her head. To be torn away from her friends, as well as having to deal with expectations she doesn't think she can realize, is almost more than she can bear.
To complicate matters further, she's constantly confronted with the real Jade, the waking Jade, the one who created her. In each other, they see things about themselves they either can't or don't want to acknowledge; Jade shows the bravery, the self-confidence, the overwhelming love for her friends that Jadespite thinks she's lost, whereas Jadesprite manifests the desire to just give up that Jade tries to bury. While Jade can get over this by determining herself further, Jadesprite just sees it as a reason that she's inferior- if Jade can go through the things she has, and come out stronger, why can't she? She thinks there's something severely wrong with her, and it makes her feel even worse about her life.
But, of course, there's a Jadesprite beyond this, the Jadesprite buried beneath the depression. At her core, she's still Jade- She's kind, compassionate, a little bit brave, and quirky as heck! But they've had different experiences. Whereas Jade was raised on an island by her dog, Jadesprite had all of Prospit as her playground, and no worries at all beyond attempting to wake up John- She's very carefree, with no objection to doing very silly things such as dancing or goofing off at inopportune times. Which isn't to say she's entirely careless! She's still very dedicated to her friends, and would do more or less anything for them.
However, due to her memories of Jade's waking life being very fuzzy, her natural intelligence isn't put to use in scientific things- She comes across as a bit of a ditz, since she's really not been taught formally (or even by herself, like Jade presumably was), and seems to lack common sense at times. She's not entirely without it; she still knows to eat and to help her friends when they're falling and almost getting crushed by moons, but she is fully capable of forgetting, for instance, that you shouldn't eat food out of the garbage. She's kind of a space cadet, a dreamer- which makes sense. Since she was a dreamself.
Underneath the depression she's a brave, helpful girl, who'd like nothing more than to do what she can for the people she cares about, and have a good time, like most people. The depression is permeating, but even the saddest dog can be cheered up with a good romp in the grass.
Also, she is still part dog, and this manifests itself in a verbal tick where she tends to start barking mid-sentence, or after a sobbing fit in place of a hiccup. It's safe to assume, based on this and the other sprites taking personality traits from both halves of the prototype, that she'd be inclined to... other canine activities. Digging up bones? Totally going to happen.
Jadesprite is canonically described as "at least a little omnipotent". She herself has only been shown to be able to teleport herself and objects, fly, and unleash waves of energy that seem to be more like pressure than actually anything damaging- Becquerel, however, prior to being prototyped with Jade, was shown to be able to cause tremendous nuclear explosions capable of destroying other slightly omnipotent creatures, so there's no reason to assume Jadesprite can't do the same.
Additionally, it's assumed she can use a rifle with at least reasonable proficiency, since Jade can, although she doesn't possess one herself. And also she's a dog, which would give her incredibly good hearing and smell, of course, probably intensified by being sort of a god.
As far as weaknesses go, her primary ones are the Green Sun constantly shining in her head and disorienting her and causing her pain, and her being a gigantic crybaby who never does anything. She's also somewhat of a klutz, since she's Jade and all.