Several others have posted fine links which describe the Prius' "eCVT"... thanks to all.
Let me add my own nutshell description, using a familiar effect many folks might have witnessed for themselves, that might illuminate how a simple planetary unit can act as a CVT:
Have you ever seen a conventional car, say a '63 Dodge or some other stone-simple vehicle, up on a lift with its engine running? Or attempting to accelerate on an icy patch? The engine spins the driveshaft, and if traction is equal at both rear wheels, then both spin identically. But if one has more "grip" than the other (either because it's on a comparatively dry spot, or because the mechanic is holding onto one wheel with the car on a lift) then the wheel with the lesser grip will do all the spinning.
That's how a conventional differential channels power from the engine.
That's also how the Prius' power-split device (aka "electronic CVT") works. Kinda/sorta: Imagine the gas engine in place of one wheel and an electric motor on the other. The driveshaft, then, becomes the output (instead of the input, as in the '63 Dodge). You can now run the gas engine at whatever speed you want and still get the desired output-shaft rotation rate by varying the speed (and direction) of the electric motor, either contributing power or taking it away depending on the circumstances. This means you can use an Atkinson/Miller-cycle design for your gas engine (or a direct-injection diesel) and take advantage of its higher thermodynamic efficiency while accommodating the peaky powerbands characteristic of these designs. It also means you can dispense with an alternator, since the motor can act as a generator. It also means you can eliminate the starter motor, since the motor can spin the gas engine if you hold the output shaft steady. And, by putting another motor on the output shaft, it ALSO means you can drive the car electrically when you want, or capture kinetic energy through regenerative braking. Being able to drive the car electrically means no reverse mechanism is needed either.
See how a simple differential lets you eliminate all that stuff you used to need? Transmission, clutch or torque converter, alternator, starter... and so on. Each elimination means a whole cascade of weight savings and loss reduction.
It's flippin' brilliant, and my real point is that it's a radical simplification of conventional automotive design, contrary to the picture painted by idiot journalists who wouldn't know a differential from a Dove Bar.
You can also see why I rebel at calling it a "CVT". There's no friction belt, for one thing, which is what other CVTs use. (All right, so Audi uses a compression belt, so sue me.) I don't trust 'em. They wear out, they're touchy about torque, they're stratospherically expensive to repair, and they're lossy. The only reason you're seeing them in other cars is as a kludge to allow their engines to run at peak efficiency, which luckily more than offsets the inefficiency of the friction belt. Talk about a technology demonstration! They're practically a science-fair project, IMHO. The Prius power-split device makes way more sense and is way simpler. Mark my words: there's a good likelihood that belt-type CVTs will be a dirty word in five years or so, when the first wave of disgruntled owners sees their transmissions disintegrate at 80,000 miles. Do the Prius a favor and help me stamp out "CVT" as a description of its technology!