The guard period after each rectangular pulse carrying the modulated data symbol is a simple and efficient method to deal with multi-path reception.
The cyclic prefix (CP) simply consists of the last part of the following symbol.

The size of the cyclic prefix field depends on the system and can even vary within one system. Cyclic prefixes are used by all modern OFDM systems and their sizes range from 1/4 to 1/32 of a symbol period. Most receiver structures use the cyclic prefix to make an initial estimation of time and frequency synchronization  which including pre-FFT synchronization, non-data assisted synchronization for Cyclic prefix in LTE

A receiver typically uses the high correlation between the cyclic prefix and the last part of the following symbol to locate the start of the symbol and begin then with decoding. In multi-path propagation environments the delayed versions of the signal arrive with a time offset, so that the start of the symbol of the earliest path falls in the cyclic prefixes of the delayed symbols. As the CP is simply a repetition of the end of the symbol this is not an inter-symbol interference and can be easily compensated by the following decoding based on discrete Fourier transform for Cyclic prefix in LTE.

Of course cyclic prefixes reduce the number of symbols one can transmit during a time interval. This method to deal with inter-symbol interference from multi-path propagation is theoretically sub-optimal. CDMA with RAKE receiver for instance provides a much better efficiency. On the other hand non-ideal implementations of RAKE receivers also degrade system performance drastically but still require a lot of hardware capacity for the basic implementation for Cyclic prefix in LTE.

The rectangular pulse with cyclic prefix requires far less hardware, so the free capacity can be used to implement other performance optimization techniques like MIMO.