All the manual says is use the button when towing or carrying a heavy load in hilly terrain or something like that. My manual doesn't explain what it does.
Just from my observation, the tow/haul button on my '13 ram 1500 does the following:
locks out MDS (no more ECO mode)
locks out overdrive (although mine won't seem to shift higher than 4th gear while towing)
favors lower gears while accelerating (takes longer to upshift)
coasting down a hill, it does not downshift unless cruise-control is active
automatic downshift when I apply brakes after being in cruise-control
From what I've read on the Internet, T/H actually causes the six-speed transmission to shift its entire range one ratio lower, enabling a "hidden" lower 1st gear. Don't know if it's true or not.