Broadband is a synonym of "Wideband". These are engineering terms.
In engineering terms, any medium is Wideband if it can carry a "big band" of frequencies.
For example, in older days cables used for
TV could carry only a few MHz of frequencies, that limited number of channels that could be transmitted over those cables. If you transmit more channels there will be a crosstalk and voice/video of one channel might mix into another.
Cables that are used today can carry hundreds of channels simultaneously.
A typical TV channel requires 6 MHz band. So any transmission medium that can carry frequencies from 500 to 600 MHz can carry 16 channels at max.
Another medium that can carry frequencies from 500 MHz to 1000 KHz (1 GHz) can carry much more channels.
A diagram of band usage in US is given here :
http://www.ntia.doc.gov/osmhome/allochrt.pdf
So Broadband is any medium that can carry large amount of information.
In digital terms that translates to any medium (cable/DSL/VSAT/....) that can carry large amount of data.