Heel & toeing is most often used in road racing, like Tim said. Usually used to downshift smoothly from say 5th gear to 2nd gear. You clutch w/ the left foot, while breaking w/ the right toe (otherwise you'll be going way too fast for 2nd gear), while also heeling the accelerator to blip the RPMs way up to where they'll need to be in 2nd gear. Then you go through the turn, and are already in 2nd gear to power out of it hard.

I think if you do a search on google for performance manual driving or heel-toe or something like that, you can probably find little video clips of an instructor driving along demonstrating the technique.