1. To slowly take over someone else's space without them noticing it.
2. To make someone believe you said something or had an idea which wasn't originally yours by changing the way the idea is said slightly.
"That guy is doing a moe. He's put all his stuff in my desk."
Guy: "I think we should unplug the cable and the re-wire the office"
Moe: "No...that wouldn't work"
Moe: "Let's disconnect the cable and redo the wires in the office"
Guy: "That's what I just said, you just did a moe!!!"