How do i read the graph editor?

I usually use the graph editor to change the curves to constant animation, or to make shapekey drivers.

However, whenever i’m messing with the curves, i just kinda move things around until it works. I don’t really understand what it is that i’m changing, i just know that these combinations make this ‘thing’ work.

At the moment i’m trying to create a GUI where i have a selection of planes that i want to be visible when a certain empty hovers over that plane.
In other words, when the empty is moved onto that selection in the GUI, it toggles on the visibility of a corresponding plane somewhere else in my scene.

 What i have done is add a driver to the visibility of an object. Set the driver to be an Sum value, based on the distance of two objects (the plane and the empty).  and it works! ....however, not when the empty is in the right spot.

 I've changed the values all over the place, examined the F-Curves, all sorts of trial and error.. And i can get the visibility to toggle on in different places, but i can't seem to get it in the right spot (the plane's origin point)

Overall what i’m asking here is how can i read the Graph editor so i can know what it needs rather than using trial and error?
What do the X and Y Coordinates represent in my scene? why is there a Time/Frame variable if what i’m trying to do is not time related?

Thanks in advance <:x