Most spacecraft are limited in their range and capabilities by consumables. What usually happens is that spacecraft need fuel to go places and turn into very useless (and very expensive) asteroids as soon as they've exhaused their propellant. This is why we've been looking for new and better ways to keep spacecraft running longer, but the best that we've come up with (ion engines) still run out of reaction mass eventually. The appeal of the solar sail, then, is that by using the sun itself as an engine, it never has to worry about running out of fuel.
A spacecraft propelled by a solar sail works exactly like a boat propelled by a fabric sail. In the boat's case, the wind consists of air molecules, while in the spacecraft's case, the wind consists of radiation pressure from the sun.
In both cases, bigger sails make you go faster, and by being clever about how your sails are positioned, you can travel in just about whatever direction you want. The biggest difference between a sailboat and a solar sail is in the scale: because the radiation pressure from the sun isn't a whole heck of a lot, you really need a staggeringly large sail to get anywhere, and even if you have a staggeringly large sail, you still won't be able to accelerate that fast. It doesn't really matter, though: if you can manage to accelerate at just one millimeter per second, constantly, after 12 days you'll be travelling at 2,300 mph. And you won't be using any fuel to do so, just the power of the sun.
We may not be at "staggeringly large" quite yet, but the new solar sail that NASA will be launching in 2014 is the largest we've ever sent into space: it's nearly 13,000 square feet in size, which is about a third of an acre, but at 5 microns thick it only weighs 70 pounds. When all folded up, it's about the size of a dishwasher, and once it gets to space, it's going to have to unfurl itself, which is the trickiest part of this whole business. If all goes well, the sail is destined for a point about 3,000,000 kilometers from Earth, at Lagrange point 1.
NASA has decided to name the mission "Sunjammer" after Arthur C. Clarke's 1964 short story about a race between solar sail spacecraft. And that's not the only science fiction connection: while Sunjammer is just a test mission and doesn't carry much of a scientific payload, it will be taking with it the ashes of Gene Roddenbery and his wife Majel Barrett Roddenberry. Warp speed may be a bit too much to expect from Sunjammer, but on the other hand, maybe not.
You can read Arthur C. Clarke's Sunjammer in the 1964 issue of Boy's Life magazine, here.