An isolation transformer is an electronic component that keeps the power going to a component isolated from the rest of the equipment on that circuit. Generally these transformers are used for items that pull a lot of current and convert it internally to extremely high voltages.
The only kind of isolation transformer I have hands on experience with are the ones used for open frame monitors. These monitors use insanely high voltages internally, and cannot function without an isolation transformer (which looks like a heavy little pile of steel plates). Plugging one of these bad boys directly into the wall will blow a fuse (if you are lucky), if you aren't lucky then it will blow out the picture tube, the flyback transformer and half the capacitors on the monitor boardset, along with a nice shower of sparks and a possible fire.
Never forget your isolation transformer when it is required, and replace them at the slightest hint that they might be damaged (arcade ones tend to get rusty, and stop working right).