Users like apps to be fast. Many apps use animations to "smooth" the experience. If an animations are too slow, the app feels...well, slow. But if the animations are too fast, they may be so fast that they make the app feel "choppy" or appear as if there is no animation at all. So how fast is too fast for animations? How fast can an animation or transition be without looking too choppy or instantaneous?
Although mostly you eyeball this, 300ms - 500ms for each animation is nice for standard buttons animations, menu and anything toggled. I will increase the duration if users are not expected to toggle the element frequently, mostly landing at 1s. Timing functions are also something you want to look at as they can make animations look slower or faster.