A FET is field effect transistor.
There is A LOT to say about what this is and how it works. Entire classes (and careers) are spent on this. So if you want an in depth explination you'll have to hit the books (or internet).
To really understand how this works you need to understand a PN junction. Basically a PN junction is where you have a material that has a bunch of extra electrons connected to a material that needs a bunch of electrons (called holes). Without getting into how it works, I'll just say that when you bias it correctly (put voltage on the right side of it) it conducts and passes electricity.
In the diagram above the drain and source are of the same type (either needing electrons or giving them) and the material in the middle and the body are of the other. Between it and the gate is an insulator so no current will pass through the gate. When you put a voltage on the gate it creates an electric field. Depending on what type of voltage (+/-) you put on the gate it either pushes electrons away or pulls them closer. This then forms a channel under the gate that looks like the same type of material as the drain and source. For example, if the substrate (material under everything) is type N, it has a bunch of extra electrons. Putting + voltage on the gate puts a bunch of electrons on the gate. The electrons in the gate and the electrons in the sub repel each other until there is an area under the gate where there are missing electrons (they've all been pushed down). Now that it looks like P type material, (looking for electrons) it is the same as the material in the drain and source so electrons begin to flow between them (think of them being shorted). When you take the voltage off of the gate, however, the electrons can return back up and cut off the channel, it no longer conducts. So its basically like a switch. Obviously, this just scratches the surface of what these are and what you can do with them, the fet has revolutionized the world!
How they are made is also complicated, but in a nutshell:
You start with material of one type (p/n) then drill in a well of n type material for the drain and source. The body pin is a well of the same type as the substrate but even more heavily doped, meaning it is even more p or n than the substrate. Then you put an insulator between the everything and then add a gate between the drain and source. Add metal connections to the drain, source, and body and you have a transistor. Here is a better image. I grabbed this from wikipedia under fet. They probably explain everything better than I do, sorry.
The circuit symbols are below. NOTE: These are two of MANY!! Also notice, these don't have the body pins on them, this is because the body pin is often assumed to be tied to ground (for N type) or high (for p type).
I don't know if I really answered you question as its a VERY broad question. But if you have more specific questions, send me a message and I can help you out. Good luck.