Double-clutching is most often used by truck drivers (as in Semis) to deal with their non-synchronized transmissions. It is a sophisticated shifting technique used by some road-course racers. (As far as I know... somebody can correct me on this point...) Simplified, it is a way to get the input shaft to your transmission spinning at the speed it will need to be at when you upshift. The idea is to reduce shock on the clutch and on your synchros by spinning things up before they're under load.
Here's the procedure - assuming you're upshifting: 1) Push In Clutch 2) Shift Into Neutral 3) Let Out Clutch 4) Use Throttle to increase RPM's to where they will need to be to engage the next gear. 5) Push In Clutch 6) Upshift into next gear 7) Let out clutch
Remember: Stoplights timed at 35 mph are also timed at 140 mph