Touge is where you and an opponent race down a road (generally a narrow mountain road). One car starts in front of the other, and if the gap widens, the car in front wins. If the gap is closed, then the car in the back wins.
Go watch some Hot Version videos on YouTube. A large amount of their races take place on the touge. You'll learn a lot from there.
Just recently played NFS: Carbon for a bit, because a friend of mine insisted on playing the multiplayer... Got him hooked on FM4 instead, so he's grinding credits for me now