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Intuitively, it's pretty straightforward. ISI is the result of many copies of the transmitted signal arriving on top of each other at the receiver, each from different propagation paths (line-of-sight-path, reflected paths, etc.). This causes constructive and destructive interference depending on the time offset between each copy. The time offsets (equivalently different delays) are due to different propagation path lengths.
If everything acts in a nice, stable way (no nonlinear effects of hardware and propagation mechanisms don't change too quickly), we can use a linear, time-invariant system model and describe the propagation paths through a channel impulse response. If there is only one propagation path (line-of-sight), this means that the channel impulse response is trivial (an impulse itself). If there are additional paths, however, there will be multiple nonzero elements in the channel impulse response, often statistically characterized through the RMS delay spread.
When you take the Fourier transform of the channel impulse response, its magnitude response is only constant (flat) over frequencies if it is trivial (an impulse). Hence, multiple nonzero elements in the channel impulse response (ISI) cause the multiple received copies at the receiver to interfere differently as a function of frequency. We call this frequency-selectivity. This makes sense since we know that sinusoidal destructive/constructive interference is characterized by the phase offset. We also know that the amount of phase offset between sinusoids will, for a fixed sinusoid path length (fixed number of wavelengths), depend on frequency.
One important observation is that the higher the sampling rate of your system, the more that frequency selectivity is typically observed, since the receiver is able to better resolve individual channel paths (different copies of the transmitted signal are time offset by values larger or on the order of the symbol rate).
Another important observation is that, generally, the more that energy in the channel impulse response is spread out over time, the less correlated the frequency selectivity becomes as a function of frequency. For example, an channel impulse response that has most of its energy in one time element (one tap) will have very little frequency selectivity whereas a channel impulse response that is evenly spread over many taps looks almost random in the frequency domain.
If the bandwidth of the channel is less than the maximum frequency of the input signal (or in other words the bandwidth of the input signal) then you will have ISI or in other words the spectrum of the signal is getting degraded or changed because of which you have a corresponding change in the time domain which results in ISI. Usually if the channel bandwidth is more than one-third of the signal bandwidth ISI is tolerable. But if the channel bandwidth is much lesser then you will have more ISI and you need to have some equalization technique to remove ISI. Ideally one would like to have the channel bandwidth to be more than the signal bandwidth. Note that if you send pulses into the channel then their bandwidth is infinite which means we would like to have the channel bandwidth to be infinite. As it is not the case we usually have some degradation. During equalization you use another filter so that the product of the channel transfer function and the filter transfer function becomes flat is 1 i.e. infinite bandwidth.
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