I think the concept behind sandblasting is pretty well known. You can clean objects, frost glass, or otherwise abrade surfaces by firing a jet of water or air carrying sand at them. The sand is fundamentally tiny rocks with sharp edges, and it grinds away what you're blasting like liquid sandpaper. It's a tremendously effective cleaning tool. Strips paint lickety-split for one thing. Any time a softer material is on top of a harder one, blasting is a possible way of getting it off.
There are some downsides, though. One, it uses rocks, which are very hard, so you can eventually grind anything off with a sandblaster. Paint or slime comes off very quickly, but whatever's underneath is almost guaranteed to be ground away as well, at least a little bit. That's why you can frost glass with a sandblaster.
Two, whatever's getting blasted is going to get hot, especially with an air jet sandblaster. There's a lot of friction involved in sandblasting, and that heat can warp or deform the object being blasted.
Third, it's messy! You've got sand (or wet sand) spraying all over the place. If you're blasting paint, you have toxic waste disposal issues, since the sand becomes contaminated with the paint particles (in addition to the paint itself).
My father bought a blaster for stripping paint from car parts, but it's not a sand blaster, it's a soda blaster. He told me that using soda as the abrasive is easier on the metal parts because it's not as scratchy, and heats them up less. It's also probably a bit easier to clean since soda (sodium bicarbonate, aka baking soda) is water soluble.
Some other related systems are blasting with walnut shells or steam.
Cryoblasting is only partially related to those two systems. Instead of sand made from silicon dioxide or some other rock, a dry ice blaster uses "sand" made from grains of dry ice. The dry ice pellets are not abrasive. Frozen carbon dioxide isn't very hard to begin with, and when it hits the surface to be cleaned, the combination of hitting a hot (compared to the dry ice) surface and the shock of impact sublimates it almost immediately.
So if it's not really hitting all that hard, how does it get paint or gunk off the surface? That instant transition from solid to gas does a couple of things. First, it absorbs heat from the surface it hits. Because sublimation absorbs heat so quickly, the temperature differential is huge, and thermal shrinkage causes stress fractures at the point of impact, or as the web site says, "The high shear produced over a very brief expanse of time causes rapid micro-crack propagation between the layers leading to contamination and/or coating final bond failure at the surface of the substrate." The paint shrinks down and flakes away from the surface it's on.
That heat went into turning the pellet into a gas. As a solid, it was about 800 times more dense than air. As a gas, it doesn't want to stay that way, so it expands. Fast. Basically, that pellet is a micro-explosive, creating a shock wave when it sublimates. Perfect for blowing apart stress-fractured paint. It's even a "shaped charge," since the the pellet didn't have time to rebound off the surface, so the gas still has a lot of the kinetic energy that it arrived with. That means the explosion doesn't propagate spherically. It's still moving toward the surface, so the result is more of a disc-shaped explosion, along the surface. Just where you want it for blowing stuff off that surface.
Needless to say, overheating isn't really a problem with dry ice blasting. If you've got the ratio of air to pellets correct, and/or the pellet size is right, you don't really cool the object much either.
Finally, cleanup rocks! There's the actual paint or whatever you blasted off the object, and . . . nothing! The dry ice has turned to gas, and left the building. (Don't do this in an enclosed space or poorly-ventilated, area, of course, because of the danger of carbon dioxide buildup suffocating you.)
I can't think of anything I need to clean with a blaster right now, but I still want one of these things. The entire process is so clever and high-tech and just plain nifty! I don't think I'll try to rent one at the local equipment rental store, though. KSL-TV did an article about dry ice blasting used for restoring the Utah state capitol building. They conclude with the comment "Unfortunately, the process is still too expensive to consider for home use." Alas.