Bandwidth is the amount of data that can travel through one give point in an increment of time (usually seconds). The bandwidth is most commonly mistaken for the speed in which data travels, but all data travels at the same speed (speed of light). Compare bandwidth to water through a pipe. If you have 2 pipes with a 40 lbs pressure and one pipe is 3 inches in diameter and the other pipe is 6 inches in diameter, the pipe with a 6 inch diameter will move the most water. Bandwidth works with the exact same principle as the water analogy.
With web hosting the bandwidth is used according to the number of visitors to a website.
For more information see: http://en.wikipedia.org/wiki/Bandwidth_%28computing%29