Lulz is a corruption of LOL, which stands for laughing out loud, which is a shitty in-cabal forced meme used by the denizens of Encyclopedia Dramatica. As defined by them: "Lulz are the reason for Anonymous' existence; everything Anonymous does is for the lulz. Truly epic lulz come from raids and invasions. Habbo Hotel and MySpace seem to provide an endless source of lulz to Anonymous, but raids of smaller websites and forums seem to have a much more limited shelf life. Regardless, "doing it for the lulz" is considered sufficient justification for any action, no matter how perverse and offensive. Unfortunately the FBI disagrees, so /b/tards in pursuit of the lulz must always beware the 4chan Party Van."
Lulz enjoys an interesting history for a fairly straightforward meme. MySpace and Xanga users really do spell LOL as "lolz" and for this reason saying "lulz" made you sound borderline retarded, even in jest. Something Awful users were banned just for using the term. It was commonly used on Encyclopedia Dramatica -- no surprise, considering the quality of their users. After the FOX11 video about "lulz" regarding the infamous Alex Wuori case, the term gained enough irony to become a forced meme and it entered the 4chan mainstream, marking the start of Newfag Summer.
People who use the words lolz or lulz are disgusting and should be shunned from humanity.