The right side of the court from each player's perspective. Points that start at deuce (40-40) are served from this side, which is where the name comes from. Also where the first point of every game begins. If you're right-handed, your forehand is the more natural return from the deuce court, which is why returners often feel more comfortable here.
"Serving from the deuce court, he goes wide to the forehand. Big first serve."