Difference between the use of 'bandwidth' in DSP and computer networking
They both define the amount of data you can get through a channel -- the channel bandwidth, together with the SNR, defines the channel capacity $C$, which has the unit of $\frac{\mathrm{bit}}{\mathrm{s}}$ (which, by the way, is simply $1$ binary decision per second), giving you the maximum amount of information you can get through that:

$ C_\mathit{Shannon} = f_\mathrm{bandwidth} \log_2 ( 1+\mathrm{SNR} )$

You see, bandwidth in the signal sense just says "we can see so and so many changes per second", and you can directly translate that to bits you get through that bandwidth, if you know how well your signal gets through.