Aquarium pumps can be used to power filters, protein skimmers and add oxygen to the water.
Most tanks will use biowheel type filters that don’t require a pump, and protein skimmers are for use in saltwater tanks, so most fresh water aquariums will use pumps to add oxygen to the water or to power a decoration.
Your fish need oxygen in the water in order to “breathe” and depending on how many fish in your tank and the shape of your tank, you may need to supplement it with an air stones or wands powered by aquarium pumps. In most cases you will probably get enough oxygen in the water just by the filtration system and air exchange at the surface but with many fish or in a taller tank with less surface space you may need a little help.
Aquarium pumps can be a bit noisy so you might want to consider placement or perhaps make a housing for it so it is not on a surface where it will vibrate and drive you crazy. The pump simply plugs into an outlet and blasts out air. You hook a plastic tube to the end of the pump and put your air stone, or decoration on the other end and place it in the tank. Presto – bubbles come out! They look cool but also add oxygen to the tank at the same time.
Some aquarium pumps can be submerged but some cannot so be sure to read the instructions before trying to put it in a tank! Some have adjustable airflow, but only the simplest ones need to be used for the purposes above and you won’t need to adjust the air flow.