While your question is a bit broad, here are some basic facts.
Bandwidth refers to the amount of frequency spectrum that is being used. For example, the bandwidth of a filter is the width of that filter, in Hz, where the filter attenuation increases to -3dB relative to the inband attenuation. The bandwidth of a signal is the amount of frequency spectrum occupied by the majority of the signal's power. For example, an AM modulated carrier occupies a bandwidth that depends on the frequency of modulation. If the modulation is a sine wave at, say, 2Khz, then the bandwidth of the modulated carrier (the signal) is 4Khz. The bandwidth of a modulated signal depends a great deal on the type of modulation.
When I say "by the majority of the signal's power" I refer to common ways of defining the edge of a signal's spectrum. One common way is to define the edge of a signal in the frequency domain as the point where the signal's power drops to 20 dB below the mean power.