A lot of the documentation for Toyota's hybrid system refers to the electric power transfer arrangement as a CVT or eCVT. They like to keep changing terminology, like the latest material calling the system a self-charging hybrid.
It is a continuously variable transmission in the same sense that a switching power supply, variable transformer, or motor-generator is a continuously variable transmission which changes the ratio between voltage and current or torque and distance continuously. It is not a continuously variable transmission as commonly understood to be a mechanical continuously variable transmission so does not suffer from those mechanical limitations.
What Toyota did, at least as I understand it, was take a engine-electric transmission system like would be found in a US diesel train locomotive (diesel-electric) and couple a mechanical transmission between the generator and motor using a pair of differentials. So the mechanical transmission selects the major gear ratio and the motor-generator continuously varies this ratio between gears using a switching converter (or by adjusting the field voltages?). The advantage of this system is that the motor-generator only has to handle a fraction of the power instead of all of it with the rest going through the mechanical transmission. I assume Toyota found this configuration to have a better power to weight and size ratio or better economics than a straight series hybrid engine-electric transmission.
Compared to gasoline car transmissions, the mechanical part of the Toyota Hybrid Synergy Drive is incredibly simple and elegant. Of course, the total hybrid system is very complicated. The YouTube video linked by windsmurf covers the mechanical parts pretty well.
The only transmission element is a single planetary gear set. In brief, a planetary gear set has a sun gear, a planetary carrier, and a ring gear. In a regular automatic transmission, a brake band can stop one of the three elements, which changes the gear ratio of the other two. But what if you can control all three elements independently?
The HSD has a smaller electric motor-generator (MG1) which drives the sun gear. The gas engine drives the planetary carrier. The larger electric motor-generator (MG2) is directly coupled to the drive shaft. MG2 and the drive shaft connect to the ring gear.
Changing the speed and direction of MG1, will change the gear ratio between the gas engine and drive shaft. Since the gas engine, MG1 and MG2 are all computer controlled, you can achieve a wide variety of operating modes. The modes can get complicated as MG1 and MG2 can independently switch between motor and generator operation at any time. Mechanical power can flow in any direction between the three shafts. At the same time, electrical power can flow in any direction between the two MGs and the battery.
The HSD is mechanically simpler than typical car transmissions. There is only a single set of permanently engaged gears. There are no linkages and clutches of a manual. There are no brake bands and actuators of an automatic. There are no electomechanical actuators of a DCT. There are no heavily clamped friction surfaces of a CVT.
Even the reverse gear is missing as MG1 can directly drive the car in reverse. The only traditional element is a parking pawl.