This article at howtogeek explains it a bit (rather indirectly). As you may already know or have guessed, animations take up CPU cycles. How much, depends on this value.
Think of a flip book: If you want to make the animation look smooth, you need many pages. If you don't care, you skip some – but still take the same time from the first to the last page.
That's about what "animation scale" is about: the higher the value, the more "pages" will be used. Thus, when you lower the value, less CPU cycles are used – leaving more of them to "other stuff".
Other resources explaining this include androidtipsandhacks:
The Window animation scale, Transition animation scale and Animator duration scale all control the duration of the animations that appear as you open windows and switch between screens. The longer the duration the smoother they appear, but if you set them to be shorter (or even off altogether) the device feels much snappier.
Set the Window animation to 5x then tap the Transition animation button to see its immediate effect. We recommend .5x for all.
(see, they also recomment 0.5x). LiveHacker even recomends to turn them off altogether.