Channel is the medium through which signals propagate from a transmitter to a receiver. If there is an ideal channel, the receiver receives the exact same signal that the transmitter transmits. However, no channel is ideal. Channel characteristics change with time and/or frequency. Rarely, channels might also be constant over time and frequency. Either way, there is some attenuation/delay introduced by the channel. Modelling the channel is to find out how much attenuation and delay has been introduced by the channel on the signal.
Taps are used in modelling an LTI channel as a filter. The number of taps and the weight of each tap typically indicates how much delay and attenuation is introduced by the channel, respectively. The number of taps also depends on the sampling frequency of the transceiver system.