Whatever a robot decides to do, an actuator carries it out by converting energy into movement. Electric motors are precise and clean and dominate most robots; hydraulic systems deliver great force for heavy work; pneumatic ones are simple and springy but harder to control precisely.
The choice shapes a robot's character, how strong, how fast, how gentle it can be. Matching actuator to task is a core design decision, because a mismatch leaves a robot either too weak for the job or too clumsy for delicate work.