Homestuck is a webcomic about four kids. They only know eachother across the internet, and each lives in a different timezone of the US, but they're all best friends. One day, on the main character's birthday, the four start to play a game called Sburb. This game, in an incredibly circuitous, time-bending manner which defies all laws of causality, brings about the end of the world through a cataclysmic series of meteor impacts. However, before the kids are taken out by this, they, their homes and their guardians and parents are sucked into the Sburban game world, "The Medium".
Throughout their time playing this game and helping each-other, they are helped from behind the scenes by their guardians, who one-by-one reveal themselves to be capable of superhuman feats.
People who play Sburb have what are called "Dreamselves", entities which wake up in distant reaches of the Medium when the players sleep. One of the characters, Jade Harley, has what is known as a Dreambot, which allows her to interact with the real world at the same time she's in the dream world.
Throughout their adventures, the characters are helped and hindered by a group of 12 "Trolls", troll-like aliens from another time and place who played and beat the game before the main characters. One of the trolls, Aradia Megido, is actually deceased due to events explained in Act 5 of the comic. Her essence currently inhabits a "Soulbot" so that she may interact properly with her surroundings.
As for genre? The creator says it's the webcomic equivalent of a crossover between Earthbound, Spore, and The Sims. You could also say it's action-adventure-romantic-comedy.