The human heart IS a pump. In fact, it is a double pump.
A mechanical pump takes in a substance, usually water, in one end and pushes it out a different end for the purpose of moving the water out of one area and into another. In a boat, for example, there is always a pump to remove excess water from the bottom area of the boat and pump it back out into a lake or the ocean so that the boat functions more efficiently and maintains its buoyancy.
The idea here is that the pump sucks the water from one area and dumps it into another area.
The heart does the same thing. Incoming blood from the body enters the heart in the right and left atria. The atria contract, forcing the blood into the right and left ventricles. That forces the blood towards either the lungs (right ventricle) or out to the body (left ventricle). As with a mechanical pump, blood is moved from the veins (incoming blood) and out to either the lungs to pick up oxygen and get rid of carbon dioxide, or out to the body to send the oxygenated blood out to nourish the cells of the body.
The blood is moved from one area and sent to another (sucked in from the veins, pushed out through the pulmonary arteries or aorta), just as water is moved from one area to another by a mechanical pump.