How is a VHF/UHF transceiver’s “reverse” function used?

A standard repeater operates using two frequencies: it listens on an "input" frequency and retransmits the signal on an "output" frequency. Normally, your radio is set up to transmit on the repeater's input and listen on the repeater's output. Engaging the "reverse" function on your transceiver temporarily swaps your radio's transmit and receive frequencies. This allows you to listen directly to the repeater's input frequency to see if you can hear the transmitting station directly, rather than through the repeater. If you can hear the other station clearly on the input frequency using the reverse function, it means you are close enough to switch to simplex communication, thereby freeing up the repeater for others to use.