A subsystem of virtually every electronic device that takes the electrical service power and converts it into some form(s) that can be used to properly power a given device. This may include turning the AC current into DC, known as rectifying (most electronic equipment uses DC power to operate), stepping down the voltage to something more suitable for low power electronic devices, and filtration to make sure they have clean power to work with. At times the voltage may be stepped up for devices that use high voltage tubes. Regardless of the specifics the overall job of the power supply is to provide good, clean power for the device.
They tend to be overlooked because of their ubiquitous nature, but the power supply is a very critical and often expensive component that can make or break a piece of audio gear. While their function, officially, is to just supply power, we must remember that this power can and will affect the way the device in question operates. Feed it dirty, unstable power and you’ll get commensurate results. “Wall Wart” and “Lump in the Line” type supplies have become popular in recent years because they are inexpensive to build and can be used on a wide variety of devices. These are generally fine for low power equipment (especially if more filtering is employed inside the device), but most high-end pro audio equipment will have an internal supply that is optimized for it.