An Axis refers to a direction of travel in world space, or a direction of orientation in rotational space. In order to move along an axis, or a three dimensional direction specified by a three axis combination, coordinates must be provided to enable said motion.
The axis is the representation of the coordinate system in use. When positioning an object, you are typically working in world space, child space, or local space, depending upon the location of the object within a hierarchy. Objects not associated with a hierarchy are said to be in world space. Objects with parents are said to be in child space or local space. This concept is important, as the numerical readouts for each axis will differ, depending upon what they are intended to show. For example, if you have a child of a parent that has not been moved, it will read X:0, Y:0, Z:0 for position. If you choose to move the child, or offset its position, you will then see the relative distance from the parent in the numerical position readout. Now, if you were looking at the same object, located in the same place but not parented, you will see drastically different information for X, Y and Z positions, as you will be seeing the actual world space location information for that object. If all you do is model or make poses, and don’t animate much, then the impact of the previous will be limited in your case. However, should you choose to animate more than occasionally, it suddenly becomes very important for you to have a good idea as to the previous. This is particularly true if you are writing expressions with Xpresso, using math functions, writing scripts or rigging characters and working with joints.