Most modern vehicles have a power steering system to assist with driving, and the power steering pump provides the power the system needs, in the form of fluid being pumped into the pressure side of the system.
Replacing a Power Steering Pump
Power steering pumps can wear out over time, even if the fluid is changed regularly. New and rebuilt pumps can sometimes be fairly inexpensive, but can be a lot of work, especially without the right tools.
Most pullies on these pumps are pressed on, and require a special puller tool to remove them; sometimes they come in a kit with the re-installation adapters, too.
Rebuilding a Power Steering Pump
Many power steering pumps can be taken apart to rebuild or reseal. Sometimes all that goes bad on a pump is the seals, and replacing the seals costs a lot less than replacing the whole pump before labor is taken into consideration.
Flushing a Power Steering Pump/System
While not as vital as it often is in a cooling system or for motor oil, flushing the power steering system is a way to make sure all of the old fluid and contaminants are fully removed from the power steering system. This will make sure the new fluid is as clean as can be, which will improve the lifespan of the pump and the rack and pinion unit (or applicable steering mechanical unit).
In this Cars Simplified video, Steve shows an easy way to flush a power steering system.