I'm coming in pretty late, but...
Are you looking for a somewhat intuitive explanation since you already have the basic mathematical definitions?
Coherence time is the time over which the channel impulse response does not change appreciably or decorrelate (with "appreciably" having different interpretations depending on what you're doing). The general idea is that if you are equalizing the channel in the receiver, the equalizer coefficients will not need to change significantly over the coherence time. If training intervals are required, the training intervals need to happen faster than the coherence time would indicate.
Likewise coherence bandwidth, for an OFDM system in particular, suggests that the frequency-domain equalizer coefficients over certain bandwidth spans will be similar. This is consistent with the definition you cited that the channel is essentially flat over the coherence bandwidth.
Both of these are statistical measures, however, as either can change quickly in a real channel and things like the spacing of nulls in the frequency domain is generally not constant.
The frequency response of the channel is the FT of the time-domain impulse response. So "coherence bandwidth" is related to the FT of the delay spread, and that delay spread is expected to stay correlated with itself over the length of the coherence time.
Hope that helps a bit.