Eees cray.
It's 9 mini-dungeons, most with unique mechanics and requiring more teamwork than the standard dungeons. When you do a "Fractal Run" you do a random selection of 3 fractals, and then your character's fractal level goes up by 1. If it's an even numbered fractal level, you also fight a special boss fractal too.
You get fractal relics from each run that can be used to buy a variety of handy things (pretty damn cheap 20 slot boxes being among them). You get a daily bonus for doing an even numbered fractal run in each fractal
tier (1-9, 10-19, 20-29 etc.). Starting at Fractal level 10, the daily bonus has a chance to contain an ascended ring, and a guaranteed Pristine Fractal Relic->10 of those, you can buy the ring of your choice.
At the moment, everyone has to do the lowest fractal any party member's max level is. So if it's a group with 3 people at level 8 but two at level 1, the group can only do level 1. This has caused a lot of fragmentation and I was decrying it within an hour of it being release. But it should be fixed by the end of the month

(You'll now be able to jump into a run at whatever level the highest available to the party is, and advance in your personal level on complete).
The 9 fractals themselves are all pretty damn awesome. Most of them are out-and-out superior to the regular dungeons and hopefully indicate a lot of promise for the future dungeon design and changes. The drop rates in the fractals once you get a few levels up is awesome. 3+ rares per run basically guaranteed at 10 and above, and a higher exotic drop rate than any other area of the game. It also scales your characters up to 80 like WvW, so you can take any character you're comfortable with (though fractal levels are per character). It's not a great source of XP but a damn fine way to get everything else.
edit: Oh yeah. Starting at fractal level 10 and increasing in intensity with each higher level, the bosses in each fractal use a new mechanic/condition called Agony. Basically it fucks your shit up proper. In all cases but one, it's completely avoidable- but if you get ascended gear (currently there are back pieces and rings), you can put in an upgrade called an infusion which gives you resistance to it when you do get hit. I've made it to level 15 with no resistance at all (though mostly because I'm lazy and haven't gotten around to buying an infusion to put in my back piece).