The graphing tool offers the usual X and Y axes, but also a Z axis. What is this for?

The Z axis allows you to add information from an additional variable to the graph, either:

Adding color (either shading by a numerical value in Z, or coloring by a category of Z)
Grouping the samples according to a category of Z. (see here)

(Sorry, it doesn't make a 3D graph. Yet.)

Here is a simple example of a scatter plot, where a numerical Measurement on the Y axis is divided up into two groups on the X axis.

Let's say there was a third, numerical variable (column), Age, and we want to see how it relates to the other two. Add it (Age) as a Z variable:

Here is the result. In this case, you can clearly now see that Age and the Measurement are correlated:

A couple of things to note:

The Z variable is now controlling the color, so the coloring due to the X group has been removed.
The Z variable was numeric, so the color applied is a linear shading.