Computer scientists might define bandwidth in terms of baud. Baud is the number of state transitions per second the line will handle. A state transition is a change of voltage on the line. When we a modem running at 9,600 baud, we mean it is capable of making 9,600 state transitions in a second. The baud rate for a given medium closely related to the bandwidth in hertz.
Network engineers talk about bandwidth in bits per second.
To them, bandwidth is a measure of how much data can be transmitted. They will talk about kilobits or megabits per second. A kilobit is thousand bits, a megabit a million. The transfer rate in bits per second is dependent both on the characteristics of the physical medium, and on the method used to encode the data being transmitted. Bandwidth measure in megabits per second will differ from bandwidth measured in hertz because different things are being measured.