The left side of the court from each player's perspective. Points played at advantage (ad-in or ad-out) are served from this side. For right-handed players, the backhand is the more natural return on this side. In doubles, the player returning on the ad side often handles the pressure points since advantage points and tiebreak points alternate here.
"Big point on the ad court. Ad-out, break point. She goes wide to the backhand."