Basically, it lets you steer a beam very precisely in an arbitrary direction, as if you were physically rotating the transmitting antenna.

Usually you'd need to rotate the antenna or else use a large number of controllable phase-shifting elements to send an output beam in the desired direction. But a Rotman lens lets you use a small number of phase shifting elements to merge a small number of source beams (still > 1, though) into a single precisely-steered output beam.