1) The sound of a Brain-fart, usually when a fairly smart person says something that's rather silly by accident or the wrong word or can't think of what to say.
2) Breaking something or crashing into something due to thinking too much.
3) Being silly and not caring what other people think of you. See dork
"It'd work better if you used contrasting colors. No, not contrasting -- Contrasting. Not contrasting! You should use contrast-gah! Do you know what I'm trying to say?"
"Derp! YES! THANK YOU!"
"Did you hear the professor walked into a wall today while working on his latest thesis?"
"Ha! No I didn't. He's such a derp"