.Hack revolves around a computer game called "The World" Its a MMORPG created for AltimitOS, the only OS to survive the PlutoKiss virus which wiped out the internet everywhere in the world for 77 mins. Altimit was the only OS immune to the virus. Because of this the internet was severly restriced for all systems except those running A.OS. Since "The World" was the only game for that system, many users became hooked on the game even after normal internet activity was restored.
You'll soon meet Aura, an AI, who was designed to be the "daughter" of the programmer, whos love died before they could have children. Aura was designed to become the ultimate AI, and "feeds" off the emotions and thoughs of the players. Moganna Mode Gone, AKA Morganna, is the AI incharge of gathering the data for Aura. The ability 'Data Drain" causes files to corrupt, trapping the players into the game, and forcing their bodies into a coma. Yasuhiko (Orca) is trapped in The World this way.
Morganna was created too intelligent however. She knows that after Aura becomes complete, she will lose her purpose for existing, and trys to stall the project however she can. The "Twilight Incident", a.k.a "Pluto Again" was caused by Morgana. It involved a massive blackout that took out power over the entire city.
That should give you some background. Its basically a synopsis of Hack.//Sign and what little I played of Hack.//infection.
.hack//Mutation, .hack//Outbreak and .hack//Quarantine are sequils to .hack//infection.