What is the difference between 'drive' and third gear?

Some automatic transmissions have 4, 5 or even 6 gears. "Drive" just means the transmission gets to pick whichever gear is appropriate; If your shifter has a "3rd gear" selection, it limits the transmission to pick from gears 1, 2 or 3. It can be used to accelerate uphill better, or when towing a trailer.