The lawsuit alleges that an excessive number of Xbox 360 consoles have experienced hardware failures, aka the RROD. Perhaps more damning is the lawsuit's allegation that Microsoft knowingly manufactured faulty Xbox 360 consoles, and then concealed the failure rate in order to better compete with The PlayStation 3 and Wii.
As evidence, the lawsuit presents articles from a variety of gaming publications, including dailygamesnews.com, VentureBeat, Digital Media and Yahoo! Each of these articles states that Microsoft knew as far back as November 2005 that over 50% of Xbox 360 consoles were defective (emphasis added because that's an insane number in an industry where 3% or so is the accepted norm).
Lastly, the lawsuit seeks a court order that would force Microsoft to pay off the disenfranchised Xbox 360 owners with all profits that it made from sale of the console. A kind of RROD refund program, if you will.