Does f(2+∆X) have any special meaning? Or is it just a standard function substitution?

Umm
delta x or *triangle*x means a change from one x to another.

I think in that concept, I would say its f(x) that transformed 2 to the left on a co-ordinate graph.
If you don't understand what I wrote above, then just treat it as a normal substitution, and you'll learn soon enough.