A coolant pump is a type of pump used to recirculate a coolant, generally a liquid, that is used to transfer heat away from an engine or other device that generates heat as a byproduct of producing energy. It's basically a very simple centrifugal pump containing an impeller within a metal housing – the pump is driven by a belt from the crank and the pump's impeller forces the liquid out of the pump. The action of it forcing the water out, draws more water in.
A mechanical pump as fitted to most engines runs continually, or at least all the time the engine is running. Symptoms of a bad coolant pump includes engine overheating, coolant leakage, coolant pump pulley making whining sounds etc.