The User Interface (UI) is the part of the game mechanic the player uses to interact with the game. The term generally refers specifically to the buttons, windows, and other controls the player sees when playing the game.
In many games, the developers made allowances for enterprising players to craft their own unique look-and-feel for their gamespace. The player can modify ("mod") just their own client application, or one can upload one's UI mod to one of the many fansites that host file transfers. Players can also download mods by peers and use those UI mods with their client. In World of Warcraft, mods are called AddOns.
By swapping out UI mods, the entire gaming community has the opportunity to find a UI that works for their playing style.