In order to predict when a volcano is going to erupt, and how bad that eruption is going to be, it's helpful to have a picture of what's going on deep down inside the thing. Seeing as we don't have any volcano-sized x-ray tables lying around, scientists have simply started using the entire universe, and the cosmic rays that it produces, as an imaging system.
Cosmic rays are high energy particles that come crashing into the Earth's atmosphere from outer space. This is happening a lot, all the time, and when one of these cosmic rays hits an atom in the atmosphere, it smashes itself into a muon, which is a tiny little subatomic particle similar to an electron. Over the last minute or so, about 10,000 muons passed straight through your body, but I'm guessing that you didn't notice, because they're generally not harmful.
Even though most muons pass right through you (and everything else, for that matter), every once in a while one of them has the misfortune to smash into an atom and it stops. And the denser something is, the more likely a muon is to run into it (since there are more atoms for it to hit). This is the same basic principle by which the x-rays that you get at the doctor's office work: there's a piece of film, and it gets exposed based on how many x-rays pass through your body and hit it. Since the denser parts of your body like bones stop more of the x-rays than floppy bits like tissues, you can build up a picture of your otherwise invisible insides.
With muons, it's possible to use a very similar technique to take x-rays* of just about anything of any size at all, including volcanoes. Instead of film, two parallel muon detectors are placed somewhere near a volcano, and muons are tracked as they pass through. By comparing the locations on the two detectors that muons hit, their trajectories can be traced, and the number of muons that have passed through the target (the volcano) are recorded. Just like with an x-ray, you'll get fewer muons passing through denser rock, and with enough detectors scattered around the volcano, you can gradually build up a 3D picture of what's going on inside.
This technique has been used to successfully map the "throat" of Mt. Vesuvius, which has been making Italians who live near it understandably nervous for the last several thousand years. NOVA will be running a special show on volcanoes on Wednesday, and you can catch a preview featuring this muon imaging technique in the video below.
*I know, technically it shouldn't be "to x-ray," it should be "to muon-ray" or something, but let's just call it a colloquialism and leave it at that.