The old way of doing CSS animations (and the way we still do things for most properties) is for layout to do all the work. Every frame of the animation the necessary parts of the webpage are laid out (the process of converting HTML to graphical objects) and rendered (converting those graphical objects to pixels) afresh with the correctly interpolated property value. If we have off main thread composition (where each layer is rendered on the main thread, but layers are composited together on a separate thread) then we can instead layout the web page once and change the way we composite to take account of the animation. The initial implementation did this in such a way that the main thread still does a layout run for each frame, to keep its model up to date and the compositor did it's own animations too. That got the smoothness but not the speed-up. In fact, since we did the interpolating twice, presumably it slowed things down slightly. My task was to finish off the work to stop animating on the main thread (bug 780692). That is the 'throttling' bit. It has been surprisingly difficult; easily the hardest and most frustrating problem I have worked on at Mozilla. But also lots of fun.
The main difficulty is that we do sometimes need to 'catch up' on the main thread, mostly when we need to respond to some JS/DOM stuff. For example, if we have to test whether the mouse cursor is over an element with an animated scale, we need the current value of that scale to be able to tell whether the cursor is inside that element. That means that layout, which runs on the main thread, needs to have an accurate picture of the state of the animation. We call this update of layout a mini-flush. We do a mini-flush periodically (every 200ms at the moment) and when we need to have accurate information for DOM stuff. What happens during a mini-flush is that we calculate the animated values for that moment in time and post them to the compositor. It gets tricky because we want to avoid doing a full (and very expensive) re-layout of everything and only update the animating property of the animated element. It gets even trickier because it might have been a restyle which requires the animation data and we cannot start a new restyle pass while one is already in progress.
I have skipped *a lot* of the details here. There is a lot of interesting discussion in bug 780692 if you are interested in this stuff.
Currently OMTA is only used on Firefox OS. There is work in progress to port it to Firefox on Android, and that shouldn't be too hard. It should work fine on desktop (that is where I did most of the development work), but requires OMTC (which in turn, currently, requires hardware acceleration), which is a little way of for all platforms. Once we have that, OMTA should be good to go.
If you are writing a webpage, there is no way to guarantee you'll get OMTA. But you have a good chance if you use CSS animations or transitions to animate either the transform or opacity, and don't have a 3D transform on that element. For example, most of the 'windowing' animations on Firefox OS (window opening animation, window changing animation, etc.) get OMTA.