Broadband is a permanent fast Internet connection replacing Dial-up.  The connection speeds are considerably faster than Dialup in addition to cheaper.  You pay one monthly low cost for the service compared with paying for each connection.  Your phone lines are not compromised when using the service either, broadband and calls can operate on the same line at the same time.

The technology is defined as "A class of communication channel capable of supporting a wide range of frequencies, typically from audio up to video frequencies. A broadband channel can carry multiple signals by dividing the total capacity into multiple, independent bandwidth channels, where each channel operates only on a specific range of frequencies." on the Webster's online dictionary.