Tow/Haul Mode?

T/H mode normally allows the engine to rev higher before an upshift. In some vehicles it also keeps the torque converter locked more. In some vehicles it makes the transmission downshift for you when decelerating to aid in engine braking.
It really has nothing to do with horsepower. It's about vehicle control and drive train longevity. I put my Chevy truck in T/H a lot when braking, even when empty. It helps to reduce use of the service brakes. My factory original brake pads lasted about 185,000 miles.
Many people seem to be adverse to using T/H mode for it's intended purpose. I can't understand why. I've heard claims it will harm the vehicle, decrease fuel mileage, and all kinds of crazy stuff. I don't know why all the angst over a very good vehicle feature.
When towing or hauling, engage T/H mode. It's that simple. Really, I would strongly recommend reading your owners' manual.

T/H doesn't just aid in towing performance, it's better for your drivetrain, esp the trans.
I would use it anytime you tow. If there's any reduction in fuel efficiency, it's so minor it's meaningless.

Tow haul is your friend. I use it when towing and going up, down or against a headwind. Other use it all the time when towing.