From Unofficial BOINC Wiki
A signal spectrum that spans a fairly wide, to a very wide, range of frequencies. Of course, the terms "fairly" means different things to different folks. In our case, we are looking at frequencies that are way up in the spectrum and therefore our definition of broadband is vastly different than the one that your telephone company, Cable Modem, or DSL provider claims. Trust me.
At any rate, we are looking at frequency bands that have thousands to millions of frequencies (in some cases even more) in the signals we consider broadband. Looking at it another way is to say that a broadband signal is covering a lot more of the Spectrum than any signal we think is a Narrowband Signal.