Oh, goody. Two sensible people answered already. But hey, here's my long version .... Please bear in mind this is only my experience, but so far it seems to be working OK and no one's complaining about my playing (at least not to my face), so ....
Basically, on the pipe chanter you close as many fingers as you can (really "tight" pipers pretty much close off every note, which is why they are gods) and actually stop the airflow BETWEEN EACH NOTE. The fingers are pipers' primary means of articulating (separating) the notes (unless you're Paddy Keenan or someone who does amazing things with managing bag and bellows too). Since the chanter often sits on your knee, you're effectively stopping the reed, and thus all sound, for a micromillisecond. This, combined with the fact that the bottom fingers are down more often in piping, creates a staccato effect which shortens the notes and creates spaces between them, which, like Brad says, is one of the contributors to "pop."
(FWIW, I've found it helpful to think of the flute or pipe chanter as a tube with little jets of air that shoot up under my fingers when I open them and then think about closing off the jets WITH AS LITTLE PRESSURE AS POSSIBLE; the ultimate goal being to just let my fingers sort of bubble along on top of the jets in this fashion.)
On the flute, I've found the easiest way to achieve this is a combination of closing the bottom hand a little for efficiency (like pipers do -- on the pipes you open as few fingers as necessary to sound a note, which translates to keeping the bottom hand fingers down much more) and "tube stop" (this is fun to experiment with -- how many fingers do you absolutely HAVE to have up to sound a reasonably in-tune note?) and deploying LOTS of top-hand cuts.
re: the cuts. If you watch Matt's top hand very carefully (the Bucks video at
http://www.youtube.com/watch?v=dS7NxJDp4zQ is good for this) you'll notice he subtly "vents" or cuts certain notes with either the index or ring finger -- B, D, & sometimes A with the index (I think Kevin C. might cut A with his middle finger), E & F with the ring -- of his top hand. Those near-constant cuts, when flowing along at speed, are the basis of what I call the burble.
You'll also notice that Mr. Molloy's right index finger stays down through the D part and other tricky passages as well as on the "A" note. He doesn't need to be waving that F finger around any more than necessary, so he doesn't. This combination of better fingering efficiency and the staccato/"space" effect (not to mention the funky overtones!) created by more complete "tube stoppage", plus his amazing phrasing, pulsing, and breath control = perfect pop.
Anyway, in my experience, top-hand cut work is key. To learn cuts, John Skelton suggests taking a simple tune like "Frere Jacques" in D which has all the standard D scale notes in it, and separating each note with a cut. I went farther with it and started trying to cut with my top hand wherever possible on everything I played, just to get used to the idea.
If you try this and your process goes like mine, eventually you'll find that you really can use your top hand for most everything (you'll also discover why a lot of people use piper's grip, to free up that index finger), and that good cuts on E, B, A, D and F with the top hand are very useful. Then, once you get going closer to speed, you'll find these wee little cuts -- "ghost notes" almost -- create a sort of bubbling or popping sound. The importance of a light grip becomes extremely apparent at this point!
This is only how I've been going about it, but it seems to be working pretty well. I'm not to Matt Molloy's or Liam Kelly's or Dave Sheridan's -- or alas, even your average 12-year-old Sligo/Roscommon kid's -- burbleage level yet and probably never will be, but sometimes, if I'm playing nice and light (especially on an Eb) at speed I can pleasantly surprise myself.
But of course, I could be totally wrong.
Deja Fu: The sense that somewhere, somehow, you've been kicked in the head exactly like this before.
Thanks though for that terrific second track! Greatly appreciated!
I bet that was absolutely earth-shattering. Would have loved to have been a fly on the pub wall after that one. Thanks, Brad! 
