Bandwidth is the width, usually measured in Hertz, of a frequency band. It can also be used to describe a signal, in which case the meaning is the width of the smallest frequency band within which the signal can fit. Bandwidth is related to the amount of information that can flow through a channel through the Nyquist-Shannon sampling theorem.
The term bandwidth is also used, informally, and by extension from the above, to mean the amount of data that can be transferred through a connection in a given time period. Bandwidth is normally based on the frequencies used and the spectral spread of the information caried on the frequency.