Challenge Modes are the evolution of Zul'Aman bear runs and Culling of Stratholme drake runs.
Like Pet Battles, Challenge Modes are a non-gear based activity. Gear will be normalized to a set item level. Where Pet Battles are solo, Challenge Modes are aimed at small groups. Challenge Modes are also indirectly competitive. Total times will be compared, but groups don't directly challenge each other.
I think Challenge Modes will shine a spotlight on tank classes, more than any other role. I think that we will see differences in the tank classes be magnified on the forums, and one tank class will be declared the best, three will be average, and one will be known as the worst.
I think Challenge Modes will be a good addition to the game. It's small scale, somewhat transient content. The emphasis on speed means that actually completing a Challenge Mode dungeon takes relatively little time, and should take less than an hour.
I don't really know how well Challenge Modes will work with a random group, though. My gut feeling is that running Challenge Modes in the Dungeon Finder will be less fun.
But on the other hand, if you still get the Valor/Justice points, it might be better to run Challenge Modes instead of heroics after you've finished gearing up. You don't need the gear drops and the people you group with are also focused on speed. From a strictly-rewards point of view, after you've gotten your gear, there's no downside to doing Challenge Modes instead of Heroics.
That means that the "Go Go Go" people are filtered out of Heroics and into Challenge Modes. Which would make Heroics a more pleasant place to be, with people who are actually interested in gearing up and killing all the bosses.
I don't know if that will actually happen. Maybe random Challenge Modes will remain a ghetto, with most people doing Challenge Modes in premade groups, to ensure the best chance of success. The effect of Challenge Modes on the "normal" dungeon runs will be very interesting to observe.