From our (the reader) perspective, I thought it was nice how J.K said he saw himself holding a pair of socks. In the last book your realize that Dumbledore is mistake bound and far from perfection. He's always been one of my favorite characters because he's such a complex individual that has so many outstanding traits in him; who knows what he saw, but I doubt it was socks! Whatever it was I assumed that Harry wasn't ready to know or hear about it as Dumbledore has always sheltered him from the truth until he was older.