Inverse kinematics

Normally any and all animation employs forward kinematics, but such method disregards the physical world the animation is performed in and gives a slightly disjointed sense of reality under certain situations.

Most noticeable cases are when characters are standing on slopes or stairs, where they don't unnaturally tilt with the slope or partially embed themselves in it, placing their legs somewhat naturally, angling their feet with the slope, but otherwise standing upright. Besides legs, this can also be used for moving the upper body, reaching out for buttons without forcing the player to take an exact spot (usually adjusted by the game rather than requiring the player to do so). Freely manipulating objects held in hands (with the hands visibly manipulating it), and so forth.

There's also plenty of potential for misinterpreting something that looks like inverse kinematics to be it, as with sufficient number of forward kinematic animations and some rudimentary detection code the effect can be largely indistinguishable, but that's effectively a half-way solution which should count as well.