So what exactly is it?

If your front sight was hinged like a door, the hinge is the third axis.   Having the third axis in alignment means the sight housing is at a perfect 90 degree angle to the bow if you were looking down from the top of the bow.

Third axis is important if you rely on a bubble level within the sight housing to see if the bow is being held level.    If your third axis is out of alignment, when you point the bow downwards for a shot from a treestand, the bubble level will no longer read true.   If your third axis is in alignment, the bubble will stay centered regardless if you point the bow upwards or downwards, provided the bow is held level.