What is the purpose of the Control Unit and Control Unit harness for the towing hitch wiring for a 2005 Honda Odyssey?

The Control Unit and Harness are strongly recommended if you are going to tow anything that requires lights/brake controls. FYI, you don't have to get Honda control units, most businesses that sell trailers sell various name brands and can do the wiring for you. Anyway, the wiring for the taillights and brakes lights of the vehicle are not strong enough to carry enough power to supply the electrical on a trailer (very dim-could cause a short). The Harness connects a power source (battery) to the trailer wires. The Control Unit is connected to the vehicle wiring as well as the Harness. When you step on the brake pedal, the Control Unit senses it and allows the power to go to the proper wiring on the trailer directly from the power source, therefore you will have brighter lights on the trailer. The same for parking and turn indicators. This is worth the money. I have this set up on my 2003 Odyssey.