"That's what she said" is a joke and subsequent meme, popularized by the US version of The Office but preexisting in Rules of Engagement, Wayne's World, and Beverly Hills Ninja. As with a number of internet memes, it has subsequently been absorbed by Every High School In The United States. Use of the phrase on "The Office" is symbolic of said show's place in popular culture: it is unoriginal, uses an excellent concept repeated ad nauseum, and has been stolen and made crap by teenagers. Here's the basic setup, from an episode of The Office in which callous boss Michael has been restricted from workplace humor. He makes the announcement to his office:
Michael: In the future if I say something funny (...) I will no longer, ever, do (that
Jim: Does that include "that's what she said?"
Michael: Mm-hmm. Yes.
Jim: Wow, that is really hard.
Michael: Tense silence
Jim: You really think you can go all day long?
Michael: Panicked, tense silence
Jim: Well, you always left me satisfied and smiling.
Michael: That's what she said! Laughs maniacally.
As is common with formerly generally entertaining things, it is now carving its way through the American High School system, often in collusion with the "Your Mom" meme. You will, on occasion, encounter a "that's what your mom said." This phrase is extremely dangerous. Do not approach, and call the humor police immediately, for fuck's sake.