I don't understand why my opponent resigned this online chess game, it seems like the position was slightly in my (white's) favor, but I did not have a commanding lead. 

It could be as simple as that the exchange didn't go as he'd envisioned it -- perhaps he thought you were going to play 20. Bxe7 which ends in an even exchange and didn't see the possibility of Bxh8.  Rook for Bishop plus pawn is not an insurmountable disadvantage, particuarly if the Bishop pair is retained but it may be that he didn't want to continue after he thought he was coming out with equality and found out that he was not.

Yeah -- I initially looked at the pawn being returned after the pin as well, but a simple sidestep by the King retains it -- perhaps he missed this as well.

After 21...Bxd3 the game would have been perfectly tied, points-wise, he wouldn't be a pawn down, as you say in your analysis. Perhaps he resigned because his mother was calling him to the dinner table??

First, this was a correspondence game, not a live game, so the dinner table idea is off.  And it looks like you are right, the material will be even. 

I am pretty quick to resign games when I am in a lost position, especially if I do something dumb against a superior player.  However, this is game I would not hesitate to play out.

...bxd3  (clears the way for the c pawns, attacks rook to maintain tempo) 22. Rfe1 (escapes the attack and briefly pins e7) Kd7 (breaks pin, discovered attack on h8, still holding tempo) 23. Rcd1 (trying to pin the d3 bishop) c4 (supports the bishop)

blacks pieces are coordinated, the king is centralized, he has two passed pawns and the bishop pair - certainly seems playable to me.