An unregulated PS is one that consists of just a transformer to convert high voltage AC from the outlet at about 120VAC to a lower voltage AC, via the step down ratio. It's actually a matter of the number of turns of wire on the primary side vs. the number on the secondary side. This lower AC voltage is then rectified. That means that it goes through a set of four simple diodes, that invert the negative phase of the sine wave to be in the positive. This is a very lumpy DC. It might be all positive voltage, but it goes from zero volts to peak, back to zero volts 120 times per second. So this must be corrected by putting a large capacitor in parallel with it. When the voltage goes to peak, the capacitor charges up and when the supplied voltage drops back down to zero, the capacitor discharges and tries to fill in the voltage drop until the supply voltage comes back up to peak. The stability of this system depends entirely on how much current you draw from it and how big the capacitor is. If you drain the capacitor too fast, your output voltage will drop at every cycle and you will have a lot of variation in the resulting supplied voltage. All of the above describes a simple linear AC/DC power supply.

A regulated power supply can be of a couple of different types. One way to do it is to start with what is described above and add a voltage regulator to the end of it. The voltage regulator will use some of the top end of your voltage to do its thing. Let's say you want a nice clean 9VDC. So you make a 12VDC simple linear and add a 9 volt regulator. The regulator prevents anything over 9 volts from getting to the output of the supply, so the simple linear supply behind it can vary quite a bit around 12VDC, and as long as it never goes too close to 9VDC, you will measure a very clean stable 9 volts after the regulator.

A switch mode power supply is a different thing all together. It's pretty hard to describe how it works in a single paragraph.

James.