Rigging is the process of creating a custom-sized skeleton (which we refer as an armature), which will later be bidden into the character model through a process named skinning, to make its body parts movable. In AAA quality games, character rigs often contain more than just bones. For example, controllers are parented to groups of bones in order to animate them more easily, without directly touching the bones, but at the cost of spending more time in setting up the controllers.
Sometimes, constraint modifiers are also used when building a complex rig. However, such advanced features are not supported by all game engines. Therefore, game artists have to be really sure that their game engine supports these features before using them on their art assets.