Microchips are small devices, roughly the size of a grain of rice, that can be implanted in your
pet as another line of defense in getting your animal back if it should
escape or be stolen.
The chip can be inserted via a syringe and requires no anesthesia (unless the animal is extremely high-strung.) For most mammals, it's placed between the shoulder blades where your pet can't get at it to damage it. (Sometimes, though, the chip will migrate around and appear nearly anywhere in a ring around the neck. Nearly any animal can be microchipped, from (theoretically) a small rodent to a horse or other exotic animal. While cats and dogs are most common, many people have large parrots, ferrets, and iguanas chipped as well.
The chips are read with a barcode scanner much like those in the grocery store. Any vet that microchips, and many that don't, have a reader, as do many pounds, animal shelters, and even private breeders.
Most vets charge around $65 to microchip, and this pays for the chip, the injection, and registration of your name and address in a nationwide database so your pet can be returned to you. Hopefully, you won't need it, but it's an excellent last resort for getting your pet back.