There is a front and a rear derailleur on your bike. The front one moves the chain on the front chainrings. The rear one moves the chain on the rear freewheel. They work in conjunction with your shifters.
those things that move the chain and change gears, one in the front and one in the back.
(D-Rail-Yur) This is the bike part which moves the chain into a different gear when you click the shifter. The front derailleur shifts at the chainrings/crank and the rear derailleur shifts on the cogs on the rear wheel.