From Zilvia.net:

To double clutch.

I still haven't explained double clutching. (actually, "Jus" did...) but why do you need it?
Other than being 'super cool' and being able to tell your girl friends (and guy friends) that you know how to "double clutch", it's (as I said) kind of useless while driving most modern cars (race cars with race transmissions {"dogmissions"} are excluded), but WAIT A MINUTE... this sounds a lot like heel and toe (HT) to us, doesn't it?

"I mean, you're just revving the engine between shifts... what's the point of putting it in neutral and letting the clutch out?"

Let me first say that double clutching =/= heel and toe!! You don't need to be on the brakes at all to double clutch-- you can double clutch w/out touching the brakes at all! HOWEVER, you will often (not always) use HT with double clutching. I'll get into this later.
Lets seeeeee. If you're going in a straight line and just feel like downshifting without losing speed and without making the car jerk (so you can accelerate faster/harder -- this is a good way to do it for freeway races... not that I've ever tried) then you can use the double clutching method.

First let's describe a situation with double clutching ONLY:

You're on a freeway in 5th gear going 60 mph. You're probably at 2,500 - 3,000rpm or somewhere around there.
Suddenly!!...
Out of apparently nowhere, a piss yellow Integra Type R pulls up fast to your passenger side, and the guy slows down to your speed.
Noticing his ugly colored banana-pee colored car, you look over. The stupid looking FOB in there is your nemesis in college! he stole your GF and thinks he's so cool. He also looks like AD: a dork. You hate him, but disregard him because you're "better than that".
However, he's just staying right next to you, revving his engine (puts clutch in and revs up) and looking at you like an idiot boy.
"I've had it with this loser punk kid who thinks his honda Integra Type-R is the shit!"
So you hit the clutch, downshift to 3rd gear, and drop the clutch while GASSSSing it almost instantaeously. This is the simplest and fastest way to downshift, so you figure it works.
Your car JERKS due to the difference in RPMs while going 60mph in 5th gear vs. going 60mph in 3rd gear. Originally you were at 2,500rpm, suddenly in 3rd gear you're still going 60mph, but rpms rose to 4,200rpm because now you're in 3rd gear! (remember: you dropped the clutch 'cause you wanna race and do everything fast)...
You start pulling on the jerk (AD), even though your car jerked and you shortened your clutch's life span by a few days.

AD, in the piss yellow banana type-R next to you, sees you downshift, sees your car jerk and sees you slowly speed up away from him... and decides to downshift, too.
Your nemesis (AD)
(1) pushes in the clutch,
(2)moves shifter from 5th gear to neutral,
(3)drops clutch in neutral,
(4)revs engine from 2,600 rpm [when he was in 5th gear] to 4,100rpm [exact rpm he knows he would be in while going 60mph in 3rd gear]
(5)presses clutch in,
(6)shifts into 3rd gear,
(7)drops clutch and doesn't jerk, because rpms were matched perfectly, and there's no difference between driveshaft speed and transmission shaft speed.

... Thinking you'd already beaten the Integra type-R, you're speeding up to 75mph mark, laughing to yourself, still at full throttle.
SUDDENLY!
The piss-banana-integra-type-R pulls up right next to you, and shoots by you as if you were at a stop!
The raw high-end power (VTEC) of the 205hp B18C5 engine screaming away from you is too much to take... you let off the throttle and start sobbing. You drive slowly back home and cry to your roommate, then masturbate to make yourself feel better...

Not only did you lose the race (what, did you seriously think you could beat a Type-R!?!?!?), but you also looked like a silly boy because AD knew you weren't a good driver-- he saw your car jerk when you downshifted into 3rd. Heh heh.
-----
another site here

Hope this helps.