Derailleurs are the mechanical components of a bicycle that actually push the chain from one gear to another in response to the action of the shifters. A front derailleur acts as a guide for the chain over the front chain rings, while the chain is actively engaged through the rear derailleur's pulley system. The bike's chain not only goes around the front chain rings and the rear sprockets, but also through two pulleys that are part of the rear derailleur assembly. The guide, or jockey, pulley is the one closest to the rear sprockets and can be adjusted to tweak chain tension.
Look at your rear derailleur body and note the adjustable screws. You will notice an adjustable barrel where the cable goes into the rear derailleur. You will also notice three screws that control the derailleurs movement. The high and low gear limit stop will be located directly next to each other on the main derailleur cage and on most Shimano models will be labelled with an "H" and an "L." Above these screws will be an isolated screw closer to the bike's frame. This screw is called the B-tension adjuster and controls chain tension.
Shift your bicycle into its largest rear sprocket. Make sure that the chain is on either the small or middle chain ring up front so you do not put too much cross-tension on your chain.
Check the distance between the largest rear sprocket, the gear your bike is in, and the guide pulley, the higher of the rear derailleur's two pulleys. There should be 1/8-inch between the pulley and the sprocket. If there is a smaller gap, or the sprocket is touching the pulley, there is not enough chain tension on the B-tension adjuster. If there is a gap larger than 1/8-inch, then there is too much tension.
Use a Phillips screw driver to turn the B-tension screw in a clockwise direction to add chain tension and separate the pulley from the sprocket. If you wish to lower the chain tension and bring the pulley closer to the sprocket, then turn the B-tension screw in a counterclockwise motion.