The axis snap check boxes are displayed under 'Direction snaps' in the 'Drawing Options' data panel when the various drawing commands are active. The axis snap is used to draw lines parallel with the major axes of the active drawing plane.
As you move the cursor around to draw a line, the line will change colour and 'stick’ slightly as it becomes parallel with one of the major axes:
You can use axis snap to draw block perimeters on planes of any orientation. If the plane is non-horizontal, the axis snap applies to the local coordinate system of the plane as if it were rotated to the horizontal:
If the axis snap is operating on a horizontal plane, the perimeter line will change colour to red if the line is snapped to the X-axis or green if it's snapped to the Y-axis. However if the active drawing plane is not horizontal, the line will change colour to orange for the X-axis and purple for the Y-axis.
At the building level, when the active drawing plane is horizontal, you can also snap block perimeters and construction lines to the Z-axis:
which allows you to draw horizontally extruded blocks, this process is explained under Adding Blocks
See also the Blocks and dimensioning protocols tutorial.