Axonometric means "of or relating to a method of projection in which an object is drawn with its horizontal and vertical axes to scale but with its curved lines and diagonals distorted." (dictionary.com) Break up its roots and you see it also means 'measured about an axis'.
An axonometric drawing is a form of parallel line (or paraline) drafting, which is to say not perspectival: whatever the object you are trying to depict (usually either a widget or a building) it does not fade off into the distance, or change size with respect to some imagined viewer. This is because the dimensions are described accurately (or with respect to some scale), rather than picturesquely as one would imagine seeing in three dimensions. Curves and diagonals necessarily appear somewhat distorted, since they are forced to conform to an uncanny geometry.
There are a number of axonometric forms or projections, each with a different emphasis and look. An isometric projection weights each of three visual angles equally (as on an x,y,z origin axis), so you see as much of the object's top as its left and right sides. A dimetric projection weights only two visual angles, and the visibility of the third side can be adjusted by increasing or decreasing these angles. A trimetric projection is an axonometric in which none of the axes' angles are equal. The last two forms that should be mentioned are called oblique projections, because one side is always represented with perfect accuracy, in plane with the page (or screen). The straightforward oblique would show, say, the face of a building and the walls would extend away behind it at some angle. The planometric projection depicts the footprint of an object or the plan of a building or sometimes the top of a widget with accuracy, and extends its dimensions off above or below this plane.
Axonometrics are used by engineers and architects to create usable depictions of a design.