They can be used for rehabilitation or for workouts. The oscillating type move the plate up and down in a see-saw motion that moves your body up and down and from side to side at the same time. There are different frequency settings which determine the speed of the oscillation. For workouts you would normally use a higher frequency setting with a faster oscillation and for rehabilitation you would use a lower frequency setting. They create instability, forcing you to engage more muscles and effort to maintain stability and balance through a movement, e.g. a squat. You can get a good workout in a shorter time as you are engaging a lot of your deeper stabilizing muscles with each exercise and rep. On a low setting for rehabilitation, they can help loosen up tight muscles. They can also be used to help promote engagement of certain muscles, e.g. if you have a weaker muscle on one side, e.g. your left glute is weaker than your right, you can do single leg work with the plate to encourage your left glute to engage.
In my case, the Pilates studio was looking at using the plate for rehabilitation but even on the lowest setting the frequency was too much. Also, I think the amplitude (the degree to which the plate moves up and down) was quite high, so it would feel like you were getting thrown around. The new one with the greater range of frequency settings was much better and the amplitude was lower on that machine. On the lower settings it was good for rehabilitation, but you could also use it for workouts on the higher settings. That's why it is important to know what you are going to use it for and to try before you buy if you can. They vary in frequency range and amplitude range.
Another factor to consider is that, with all the moving and shaking, the motors can wear out quite quickly, especially with cheaper models when used mostly at the higher frequencies. Also, overusing the plate can lead to neck and back pain and other issues. As ActiveAggie said, it is normally recommended to use for a maximum of 20 minutes at a time.