The Static is a common name for a global phenomenon in 2219 Stark. Recently, a mysterious effect has begun appearing on the Wire, affecting the interface between Wired systems. This runs the gamut from a nuisance - fridges forgetting to order fresh groceries and letting produce go off - to communications being interrupted and traffic control systems disrupted, causing deadly accidents. It has been occurring with greater and greater frequency.
For Zoe Castillo, however, this interference takes the form of visions on various screens, involving a little girl and a mysterious black house. She later learns, both from her own investigations and from Helena Chang, that the Static is caused by the residual trace of this girl, Faith, who is still alive on the Wire despite her physical death.
It is not known whether Faith deliberately caused this interference or not, and if so, whether she intended it to be deadly. In any case, Helena begs Zoe to return to the Winter to essentially euthanise Faith and end the Static, one way or another.
The working name for Dreamfall was The Longest Journey: Static.