Bandwidth refers to how much data you can send through a network or modem connection. It is usually measured in bits per second, or "bps." You can think of bandwidth as a highway with cars travelling on it. The highway is the network connection and the cars are the data. The wider the highway, the more cars can travel on it at one time. Therefore more cars can get to their destinations faster.
The same principle applies to computer data — the more bandwidth, the more information that can be transferred within a given amount of time.