Animatronics is the use of motors, servos, cables and electronic control to move a puppet or figure, either pre-programmed or driven live by a performer.
It sits at the point where puppetry meets engineering, and in film and theme park work it is often combined with hand puppetry in the same character.
Two ways to drive it
Radio control puts a performer on a transmitter operating servos live, so the movement is a performance and can respond to a scene. Pre-programmed animation runs a fixed sequence, which is repeatable and precise but cannot react to anything. Most screen work mixes both.
What it is genuinely good at
Things a hand cannot do. Eye movement and blinks, brow and lip detail, ear and tail articulation, and any creature whose anatomy does not accommodate a forearm. A servo can also hold a position indefinitely without fatigue, which matters on a long shoot.
What it is bad at
Spontaneity, and cost. Every axis of movement is another servo, another linkage, another channel and another failure point. A complex head can carry twenty servos and still be less expressive than a well-performed foam puppet, because responsiveness matters more to an audience than resolution.
The hybrid is usually the answer
Hand-operated mouth for the performance and timing, servos for the eyes and brows. That combination gives you the responsiveness of live puppetry and the detail of mechanics without engineering the whole face.
Getting started
is far cheaper than it was. Hobby servos, a microcontroller and basic linkage will drive a pair of blinking eyes for the price of a few yards of fleece.
The hack: build the mechanism and test it fully before you skin it. Everything is unreachable once the fleece goes on.