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A power supply is a device which filters and controls the electricity flowing into an electronic device.
The wall sockets in your house (in the US) supply alternating current at between 110 and 120 volts, but most electronics circuits require direct current at much lower levels. In addition, the ac line voltage was designed to supply raw power to large equipment, such as refrigerators, air conditioners, and other large motors. Whenever one of these devices turns on, there can be a momentary drop in the line voltage, followed by a sharp rise (or "spike") which can be reflected back down the line from one house to another. Other devices, like flourescent lights, can dump large amounts of electrical "noise" back onto the power grid. These changes (or "transients") can be reflected to other houses on your block, or all over a large city. These factors would destroy most sensitive electronic equipment, such as a computer. For these reasons, we need power supplies to regulate and condition the power.
The first device in a power supply is usually a transformer which steps down the ac line voltage to a lower level, and serves to isolate the device from a direct connection to the ac line. A basic transformer consists of two windings of wire (referred to as the "primary" and the "secondary" windings) around an iron core. The alternating current from the wall socket passes through the larger primary winding and sets up a changing magnetic field in the iron core. The magnetic field then creates a current in the smaller secondary winding. (Conversly, if you run a low voltage alternating current through the secondary winding, you will get a larger alternating current on the primary). The transformer effectively isolates the device from the ac line since there is no actual electrical contact between the two windings.
Once the current has been stepped down to a lower level, a device called a diode rectifier converts the alternating current (ac) to direct current (dc).