This is another hugely important step in reducing the cost of access to space.
First, reusing rocket stages is generally important for this, becuase rocket stages are incredibly expensive. Like, roughly $60,000,000 expensive, and that's for the cheapest rocket that will get you to orbit today. Other providers cost more. About ¾ of that is the cost of the first stage, and all launch providers currently throw every first stage into the ocean each time they launch. As SpaceX say, imagine how expensive air travel would be if we threw away every aeroplane after it was used once.
Second, although SpaceX landed a first stage back on land in December, this isn't always going to be feasible for all launches.
The hard part of getting to orbit is not going very high, but going very fast. As you can see at Second-stage Engine Cut-Off (SECO), which happens around T+09:55, the second stage is in orbit 215km up, but going 27,109km/h. 27 thousand kilometers per hour, sideways (the altitude is nearly constant). Although a lot of that speed comes from the second stage engine after it's basically got out of the atmosphere, when the first stage has done its main job at Main Engine Cut-Off (MECO, T+02:32) the whole rocket is going over 6600km/h. Although the unpowered stages gain over 10km in altitude (68km - 79km) between MECO and S2 Startup at T+02:45, they're going sideways faster than they're going up.
In order to get the first stage back to the landing pad, it first needs to turn itself around and have enough fuel left over to not only kill all the horizontal speed it's picked up, but to go back the way it came (the "boostback burn"). Then it needs more fuel to kill all the horizontal speed it picked up going back the other way (the "reentry burn", which also kills some of its vertical falling speed) in order to come mostly straight down for the actual landing (with the "landing burn").
Some launches will either have a payload which is too heavy, or which needs to go into too high an orbit, for the Falcon first stage to have enough fuel to both get it there, and return to the launch pad. Also, despite SpaceX's impressive Falcon Heavy flight animation, when they do get the FH actually flying (hopefully later this year), although the outer cores will probably be able to make it back to the pad, the centre core will almost certainly be too far downrange with too much speed to boost back.
So drone ship landings are going to be a necessary part of reusing rocket boosters and reducing the cost of access to space. And SpaceX just demonstrated that they can do it. For a look back on what it took to get here, this SpaceX Landing Montage gives a nice quick overview.
Looking to the future, SpaceX aren't planning on reflying the booster they got back from the Orbcomm mission in December, as they want to keep it for posterity and don't want to risk it with another launch. However, they did put it on a test stand and re-fire all the engines to confirm that it did still work with only a refueling and no refurbishment. But, they are planning on re-launching this first stage later this year. So that will be interesting, especially for whoever wants to risk their payload on it!
At this point, I should mention Blue Origin. On Nov 23 2015, their New Shepard rocket became the first rocket to take off from land, go to space, land back on land under its own power, potentially ready to fly again after only a refuel. Many people - well, many SpaceX fans - were dismissive of their feat, because they "only just" went to space, achieving an altitude of a fraction over 100km with no lateral speed. Comparisons were made between the New Shepard and Falcon 9 launch vehicles and their flight profiles. I think a lot of this was borne of frustration, not just because Blue Origin beat SpaceX, but because they did so while SpaceX was grounded for 6 months following the failure of CRS-7. If only it weren't for that failure, or if only SpaceX had returned to flight sooner, they could have been first!
I think those criticisms were unfair. As a SpaceX/Elon Musk fan I share the frustration, but if SpaceX had flown the New Shepard flight, I think everyone would have been talking about what had been accomplished with that flight, rather than focussing on where they felt it was lacking. Going for reusability and then for orbit (with an announced, but as-yet-unnamed future vehicle) is just a different path than going for orbit and then reusability. And as much as I may have issues with the way Jeff Bezos and Amazon do business, I have to congratulate Bezos and Blue Origin, and give them kudos here.
Shortly after, on Jan 22nd 2016, they reflew the same rocket to space, reportedly with minimal refurbishment. That's the first time a rocket has gone to space under its own power, been recovered, and gone to space again. Then, on April 22nd 2016, they did it again.
Truly, we are at the dawn of a new golden age of spaceflight.
(Thanks to everyone at /r/spacex for keeping track of all this stuff, providing links, intelligent discussion, and answers to endless questions.)