A servomechanism is like a robot that can do what we want by following instructions. It has a little computer that tells it what to do, and it uses sensors to figure out what is happening around it.
Imagine you want a robot arm to pick up a glass of water. You would tell the servomechanism what you want it to do by pressing buttons or typing on a computer. The hidden computer then goes to work by sending signals (or instructions) to small motors inside the robot's arm, telling it how to move.
Then, the servomechanism uses its sensors to see when the arm has picked up the glass of water. If it did not pick it up, then it tries again by adjusting the movements based on more instructions the computer sent. Think of it like a video game where the robot is controlled by a controller.
Servomechanisms can be used in many different places, from airplanes to robots that assemble cars. They are essential to help things move in the right way and do what they are supposed to do.