Submersible water pumps, such as the ViaAqua or Rio Aqua pumps are run completely underwater, usually in the sump of a wet/dry filtration system. They draw water from the filter, and push it back into the aquarium, or through other devices, such as chillers or UV sterilization units. There are several advantages to a submersible pump: they are easy to install because they don't require you to drill and install a bulkhead in your filter system; and they tend to be a little quieter because they run underwater.
The main disadvantage with submersible pumps, especially the more powerful ones, is that they are water cooled, so that means unwanted heat may be added to your aquarium water. Additionally, your filter's sump may have limited space for a pump, so the dimension of the submerged pump is an important consideration.