It uses the recoil of the bullet to eject the used casing and loads a new one.

http://www.youtube.com/watch?v=Ke6K-MUUJFg

the term "machine" just means the gun will fire more than one bullet at a time, with one pull of the trigger.

All semi-automatic and fully-automatic depend on gas to operate. When the gunpowder ignites, its solid mass is converted into heat and gas. The volume of the gas created is much, much greater than the volume of the solid gunpowder that was in the cartridge. The gas expands in all directions, pushing the bullet down the barrel. The gas also pushes back against the base of the cartridge (It also presses the walls of the cartridge, but they are restrained from moving by the walls of the firearm's chamber.). The base of the chamber presses against the bolt face. At this point, one of two things will happen: 1 - If the firearm is designed to be cycled by "blowback" (as in the Uzi or MAC-10), the bolt is pushed back with enough force to allow the spent round to be ejected. As the bolt's recoil spring pushes the bolt back into battery, the bolt face catches the edge of the next fresh round in the magazine, pushing it into the chamber for the next shot. 2 - If the firearm is "gas-operated", the bolt is locked to the receiver. As the bullet continues down the barrel, it passes a small hole. This hole allows some of the expanding gas to leave the barrel and travel through a very small tube pointed at the bolt. The gas in the small tube either pushes a piston that unlocks the bolt and pushes it back as described above (as in the SKS rifle) or the gas pushes directly on the bolt (as in the M-16/AR-15 rifle), continuing the operation. Strictly speaking, both kinds of actions are gas-operated, but the term "gas-operated" is used to distinguish blowback action fireams from firearms that use a more sophisticated system.

Of course, how do you think the bullets tend to be propelled?