The Diplomacy Card enforces peace between two players for a variable number of turns. While peace is enforced, neither player will be able to attack the other. The card takes effect the turn after it is played.
In games with longer diplomacy durations, you can use the "View Active" button under the Cards panel to see what Diplomacy Cards are currently affecting the game and when they will expire.
While peace is enforced, Warzone still allows you to issue attack orders against the target player. However, they won't do anything unless another player (one that you can attack) captures the destination territory before your attack order takes place.