Animation state machine
A state machine whose states are animation clips or blend trees and whose transitions fire on parameters, with blended crossfades between them.
The dominant way to drive character animation. The states are poses — "idle", "walk", "jump" — and the transitions are gated on variables like speed or a jump flag. When a condition trips, the machine slides from one state to the next with a crossfade rather than a hard cut.
Unity's Animator Controller (Mecanim, 2012) popularised the boxes-and-arrows graph; Unreal's AnimGraph carries the same idea. At heart it is an ordinary finite state machine specialised for animation, often stacked in layers so the upper and lower body can each have their own.