Just as you sample a signal to process or model it digitally, you also sample the channel's impulse response. Each sample corresponds to one tap. When the signal's bandwidth increases, you increase the sampling rate, so your channel model now has more taps.
Usually, a channel is modelled as having a single tap (flat fading) when the channel's impulse response is different than zero only for the first sample. You can then ignore all other taps, since they're zero. This means that the largest path delay through the channel is shorter than the sampling interval. The implication is that a symbol will not interfere with its neighbors.
Note that, if you oversample, you can get a channel impulse response with more than one tap and still have flat fading. Flat fading means that, at the sample corresponding to the symbol time (and all subsequent samples), the channel's impluse response is zero.