Seems to be a working memory aid for me.

If I have to manipulate equations mentally, I'll (sort of) explain the equation sub-vocally and assign chunks of it to different fingers/regions of space, and then move my fingers around or reassign to regions, as if I'm "dragging and dropping" (e.g. multiply by a denominator means dragging a finger pointing at the denominator over and up). Even if I'm working on paper, this helps me see one or two steps further ahead than I could do so using internal mental imagery alone. I don't remember explicitly learning this.