It is an OD off button for your transmission. When it is activated it prevents the transmission from shifting into overdrive. You will now only upshift to 3rd. When to use it? When pulling heavy loads and the transmission does not want to stay in OD for very long. If you find the tranny is hunting a lot between 3rd and OD. Press the button to lock out OD. Continual shifting is what will effect the longevity of the tranny.
Your RPMs will climb about 500 but will have some but minimal impact on fuel mileage.
Your Tow-haul button on your suburban is totally different. When activated, it changes the shift points so the engine stays in each gear a little longer to take advantge of the slightly higher RPMs.
Also, welcome to FTE.
S