[This is a bit long-winded, and Psion and mister k already said something, but I'm on the bus and don't have a whole lot better I can do, so here goes.]
Here's my description. (Actually the general form is stolen from the video where I learned about reportaling.)
So a bit of history. You may or may not know that Portal 1 had somtehing called the "portal peeking glitch." This is where you could step into the portal, barely through to the other side, fire, and step back through the portal before the other end hit. With practice, this is functionally equivalent to being able to fire one end of the portal through the portal, something you can't normally do. (Well, it's equivalent as long as you are standing next to an end.) You can do all sorts of things with this. As much as I like peeking, it probably really is a glitch, albeit one that's way less bogus than, say, the wall climbing/flying glitches.
Now, when Portal 2 came out, they wanted to remove the peeking glitch. It's still there from what I'm told, but it's way way harder to execute, and I can't do it. (And while I'm no Transgenic, I have played a ton of portal and am good at it.) The portal travels much much faster than in Portal 1 and there's a strong push. It's this push that is behind the reportal glitch.
I'm not sure if it still does this with the latest patch, but if you put a portal end on the bottom panel of a wall, stepped midway into the portal, then fired the other portal end somewhere, the push it gives you when the portal closed would be enough to shove you a couple steps away from the wall. (Easiest way to reproduce this: walk right up to a wall so you can't get any closer. Put the orange end in front of you, and the blue end somewhere else. Take a couple steps so you're looking at the wall almost edge-on, but make sure you're still on the orange side of the portal. Fire the orange end. Note that you have to take a couple steps to get back up against the wall.)
So, what's reportaling? The canonical case of reportaling is if you have two floor portals, and are oscillating between them. Suppose you are falling toward the blue portal. If you re-place the blue portal right where it currently is, just as you are falling into it, then you will essentially portal-peek: you will fall to the other side of the portal just before it closes. The timing on this was fairly tight, but if you got it right, then as the portal closed, it would give you the push I described in the previous paragraph. This extra push gave you extra momentum, which means you go higher. Do it again, and you'd gain more momentum.
The amount of momentum you could get isn't limitless -- there's a terminal velocity -- but if you retrofitted all of the test chambers with a portalable floor so you could do this, you'd be able to at least come reasonably close to the ceiling in any of them.
The more interesting thing about what you could do with the reportal glitch is it gave a way of solving some puzzles in a completely new fashion. With just one or two uses (as opposed to just using it to build up a bunch of momentum from floor portals). I never did this, but going through the game with an eye to where you could apply the reportal glitch would have been really cool.
The first (and really only, I haven't checked to see what clever stuff people have come up with) example of this is a reportal-enhanced solution to Wheatley's chamber 11. I can't find it, but someone had a brilliant solution, completing that chamber in 10 or 15 seconds, and it relies on one well-timed reportal as you launch yourself from the faith plate into a portal on the slanted surface.