When we dig uranium out of the ground, 99% of it is U-238, which we don't care about. 1% of it is U-235, which we use for all kinds of things, including conventional reactor fuel. Bill Gates and some of his pals figure that it would be a much better idea if we could just burn the U-238 instead.
Using U-238 as fuel wasn't Bill's idea, but it's taken until recently for supercomputers to figure out how to make the reaction work properly. Based on these new data, Gates helped fund a startup called Terrapower, which is attempting to build the first prototype of a new type of nuclear reactor called a "traveling wave" reactor.
A traveling wave reactor gets its name from how the nuclear reaction propagates through the reactor's fuel. A bunch of rods of U-238 are placed in a big cluster, and a rod of U-235 (just one) kick starts the whole thing. The U-238 gets converted to plutonium 239, which generates heat keeps the reaction going, and as the reaction propagates outwards in a sort of wave, more rods of U-238 get shuffled into the middle. And after the fuel gets all used up, you can take it out and use it to kick start a new reactor.
So basically, you can burn the expensive fuel. You can burn the cheap fuel. You can burn the waste that the fuel produces. And you can even burn the much more dangerous waste produced by other types of reactors. There's enough leftover U-238 just sitting around to power our entire country for centuries, and by extracting uranium from seawater (which is apparently easy to do), you could provide power to the entirety of civilization until our planet falls into the sun. Or at least, for about a million years.
Oh, and if you're worried about meltdowns and stuff, the Terrapower prototype will be passively cooled, meaning that it won't rely on the active cooling techniques that didn't work at Fukushima. Terrapower hopes to being construction around 2016 or thereabouts, and have the traveling wave reactor up and cooking by 2020.
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