The purpose is to flip the phase of the output should a wheel bridge a gap in the track where the two rails are of differing phase (e.g. The Rail A and Rail B connections are inverted between power districts). It also serves the purpose of a reversing unit in a reverse loop, where a booster is used to power the loop, a turntable or a live frog diamond crossing.
Some boosters have to be configured to be auto-reversing. For example, the Digitrax Zephyr can only be autoreversing if it is configured as a secondary booster by disabling it as a command station (Option switch 2 "closed"), and then enabling autoreversing (Option switch 3 "closed").