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 in.
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.