An air pump is a device used to move air, possibly under pressure. Typical aquarium air pumps move air by using an electromagnet to rapidly vibrate a rubber diaphragm. By increasing air circulation you create an under water current which prevents dead spots and some areas becoming stagnant.
The improved circulation will move highly oxygenated water from the surface lower in the tank allowing water with more carbon dioxide and less oxygen to the surface of the tank where it can release its carbon dioxide and take up oxygen. They are also used to power equipment such as under gravel filters or protein skimmers.