To outgeek someone is to hog a conversation by over elaborating on a topic or subject that the receiver is not interested in nor informed on. When you are in a conversation with someone and they talk endlessly in depth about the nitty gritty mechanics of their favorite video game that you've never seen nor care about, that is a prime example of outgeeking.
Danny: Hey, why are you so late for lunch?
Anthony: Yeah sorry, I got outgeeked by Jacob on the way he-