White's opening move of 1.d4 is referred to as the Queen's Pawn Game, this is the second most popular opening move for white. Now it's name is usually described as games which open with 1.d4 d5 (also known as a Closed Game) where white doesn't initiate the Queen's Gambit (2.c4).
White's move of 1.d4 offers basically the same benefits center control and development as the King Pawn Opening (1.e4), but unlike 1.e4 where your pawn is undefended, the d4 pawn is protected by White's queen. This small difference can have a massive effect on the opening game-play. The d4 opening is more popular than e4 with many masters.
Moving white's queen pawn out two squares is not always met with 1. ...d5, sometimes the Torre Attack might be played when black responds with 1. ...Nf6. White then plays Nf3 and black moves to e6. White now pins blacks f6 knight to his queen by moving Bg5. It is common to see black play h6 trying to scare off white's bishop, white can capture the knight then soon being captured by black's queen. White can retreat his bishop to h4 if he still wants to pin the knight, but black can just play g5 and you will be forced to move to g3 with your bishop.
Pros: Achieves the same as e4, but with added Queen protection.
Cons: Castling can be slightly more difficult.