Here’s an article about Thorium reactors I found via Nick at Fine Structure. It’s not particularly detailed, so I thought I might be able to fill in some of the gaps.

Th-232 is the naturally occurring isotope of Thorium, with a 14 billion year half-life, and the idea is that you let it absorb a neutron to become Th-233, which then beta decays twice (to Pa-233 with a half-life of 22 minutes and then to U-233 with a half-life of 27 days). The neutrons, as the article says, are produced by bombarding lead with protons, and would also be produced by fissions in the U-233. But since the mass is subcritical, this extra source of neutrons is required in order to run at steady-state and produce macroscopic amounts of power.

[T]here are downsides to the use of uranium-235 as fuel: first, it produces plutonium as waste. Second, the uranium-235 fuel cycle is what engineers call “critical”: once it gets going it’s self-sustaining, so there is a risk – albeit a tiny risk – of loss of control.

The unwanted plutonium “waste” is a byproduct of having U-238 around; most Uranium is U-238, and it, like Th-233, can absorb a neutron and beta decay twice. It becomes the somewhat long-lived fissile Pu-239. Starting with Thorium bypasses this particular issue.

The use of a subcritical mass shouldn’t be specific to this system, though. You should be able to do this with U-235 as well, but running a reactor as a critical mass is a much easier system to build.

The other advantage appears to be the fission products. The article states

[T]he small amount of toxic waste generated by the thorium/uranium-233 fuel cycle ceases to be radioactive after a few hundred years, rather than the thousands of years during which uranium waste remains toxic.

This makes sense to me; the fission products have excess neutrons and tend to beta-minus decay and with U-233 you start with fewer neutrons, so you will have a slightly different fission yield and your fission products are going to generally be closer to stability. This would also imply less decay heat, which is the issue that has been plaguing the Fukushima reactors — the radioactive fission products must be cooled long after shutdown. What the article doesn’t explain is how much smaller this is, so it’s hard to tell if this article is overplaying the operational safety improvements.