A power supply for a device that is not integrated inside the device itself — the power supply is a separate unit that resides outside the device it powers. For guitar and bass stompboxes and other smaller, low-power devices, an external power supply usually takes the form of a wall wart. Some devices also use “lump-in-the-line” external power supplies.
In the case of tube microphones and higher-end studio preamps and processors, the external power supply is usually a larger tabletop or rackmount box, which may incorporate controls of its own, such as a polar pattern-select switch.