When capturing the sound of a speaker cabinet in a studio, sound engineers select different microphones and arrange them in different placements to get a particular sound. For example, a mic can be pointed straight at a speaker or angled slightly off-center, in order to emphasize (or de-emphasize) certain frequencies that the mic picks up.
On-axis, for most microphones, is a line in the same direction as the long dimension of the microphone and will produce a noticeable difference in coloration when compared to the same microphone in the off-axis position.
In Eleven, the Axis switch lets you toggle between on- and off-axis setting of the currently selected microphone model. The default position for Mic position is On Axis.
All Eleven cabinets and mics were close mic’d (whether on- or off-axis). This provides the purest tones possible, of any room tone or ambience specific to the Eleven recording environment.