The use of cyclic prefix in OFDM to mitigate Intercarrier Interference
The discontinuity between symbols has spectral components higher than the channel width, and because individual channels are not bandpass filtered, it spreads into adjacent channels.

This still happens when the guard interval has a constant value (e.g. zero) -- you have two discontinuities then, one at the beginning and one at the end of the guard interval. The length of the guard interval isolates symbols on the same channel in time only.

With cyclic prefix, you still get a discontinuity at the beginning of the guard interval (where it doesn't matter, because anything received there is ignored), but not at the end of it, where it would affect the following symbol.