A common use of a brush motor is in a fan, for example the type that is used to keep my laptop from overheating. But what exactly is that preventing, and what does overheating do to a system such as a laptop?
The fan helps to keep internal units cooled down, heat is created when there is resistance in the different hardware inside the computer. With all the units preforming very close to each other, a lot of heat can be generated. This is why keeping any appliance that generates a lot of resistance should be turned off when not in use, they are just draining unnecessary power and can create enough heat to cause a fire if given the proper (or rather improper) conditions. The fans used by such appliances serves to cool off the internal devices to a certain extent, and don't actually create that much heat themselves, which is useful.
There are alternative ways of keeping devices cooled down, fans are one type, but there are also liquid cooling systems which are less common and even a phase change unit, which uses a cooling technique similar to a refrigerator.