Controls Algorithms are used to ensure that the physical state of a system matches its desired state. That can mean a number of things in VEX, such as velocity control, moving to a position, or holding a lift at a desired height. In its simplest form, a control algorithm evaluates the difference between the robot's current state and its desired state and then computes and output value for the motors to use to move the robot to the desired state. Using a control algorithm like PID has a number of advantages over setting constant motor values for movement, with one notable example being the ability to perform consistently even with varying battery voltages.
There are a number of control algorithms used in VEX. The most common of these is PID by far, but the other algorithms have useful applications as well.