Why is d5 the best move in this position? What is the thought process behind playing d5 in this position?
I'm not sure if it's the best one but...
First of all, it breaks black's pawn structure. Look at black pieces: Bf8, Nh7, rooks haven't moved, King is in the center. If you have safe king, developed pieces and your oponent is miles behind you, you want to open files. d5 is a move that I would do without much thinking. Such move just must be good!

After 1. ... - exd5 2. N4c3 and pawn on d5 falls. Be6 doesn't work due to simple f5. This position is much much better for White. Look at this structure. Pawn on d6, black pieces. Argh, I don't like it soo much from black's perspective. And keep in mind, pawn on g5 is hanging because of 1. Bh7 - Rh7 2. fg5 - hg5 3. Bg5.