What exactly IS vacuum forming?

It's a way of molding plastic.

The general "theory" behind it involves heating a sheet of plastic until it's very flexible, and then lowering it over a mold on a vac-forming machine/table.
Suction pulls the sheet of plastic down, over the mold, and to the table.
The plastic will form to and cool into the shape of the mold.

On a homemade table, usually the table is just full of holes and hooked up to a vacuum cleaner.
Works quite well actually.
Basically, you make a mold out of wood/ clay, and put it on a vacuum-forming table. Its just a box with a bunch of holes on top hooked up to a vacuum. Now heat a sheet of plastic in the oven until flexible, put it on the mold, and turn on the vacuum. All the air will get sucked out, and it will harden to the shape of the mold.
There is a really good instructable but I forget what it's called. Just google vacuum forming and you will find lots of stuff.