If successful, SpaceX will be able to reuse most of the Falcon 9 first stage rocket assembly.
On December 19th at roughly 1:20pm Eastern Time (weather permitting), SpaceX and a soon-to-be-richer NASA will launch a Falcon 9 rocket chock full of supplies, bound for the International Space Station. It's an astronaut-free mission, as has been the case before, but SpaceX's fifth ISS resupply trip will be special nonetheless.
Once the Dragon spacecraft capsule detaches from the Falcon 9 first stage, as is normal, the rocket will fall back down to Earth. Instead of falling down into the ocean, however, SpaceX will attempt to land the rocket on an unanchored platform floating in the water.
This kind of landing, while dreamed about by space agencies the world over, has never been attempted before. And whether it's successful or not (odds are being placed at 50-50), SpaceX will be well on its way to being able to deploy, land, and rapidly reuse rocket components. "A fully and rapidly reusable rocket...is the pivotal breakthrough needed to substantially reduce the cost of space access," said SpaceX in its blog post. "Over the next year, SpaceX has at least a dozen launches planned with a number of additional testing opportunities."
SpaceX is designing its rockets to withstand the heat of re-entry, which is why a landing is being attempted. If the Falcon 9 can land, and tests show it can be reused, SpaceX (and NASA, by proxy) could stand to save millions while launching rockets into space. Furthermore, such a landing would not only cut costs on ISS trips, but the research could be applied to other, longer manned missions to the Moon, and Mars. Landing a rocket on Mars, then using it to blast back to Earth? That would make planetary exploration easier, cheaper, and perhaps closer than previously anticipated.
SpaceX has already done several successful "soft landings," which has the Falcon 9 fire its boosters before landing in the ocean. The video up top is a land-based launch-and-land test from earlier this year.