Duplexer are needed to insulate the receiver and the transmitter of a radio frequency repeater, which usually work at the same time. This means that in most cases the transmitter retransmits what the receiver is hearing while the receiver is hearing it.

The receiving and transmitting frequencies are often close to each other, which creates problems: The receiver is desensitizes by the energy of the transmitting signal and, as a worst case, the energy of the transmitted signal can destroy the receiver.

Here comes a duplexer into play: It insulates the receiving and transmitting frequencies from each other and in many cases the receiving frequency is also insulated from many other radio signals produced at the repeater site than can also desensitize the receiver.

In theory, you don't need a duplexers if the reveiving antenna and the transmitting antenna are far away from each other. You will have huge losses in the very long antenna cables between the antennas and the transmitter/receiver. But these should be neglected in this simplified view.

The closer the receiving and transmitting antennas are to each other the more insulation do you need. See this illustration about what insulation is necessary: