A bike rear derailleur is used to move the chain from one sprocket to another of a different size. It will generally be connected by a cable which is moved by the gear shifters. It is also an important component for taking up the chain slack making sure that the chain doesn't jump off. Of course you will need to choose the derailleur which is compatible with the amount of sprockets in your cassette, but also the cage length is important. A short cage is recommended for downhill riding, a medium cage when using a double crankset and a long cage when using a triple chainring chainset.