Axes is the correct plural form of two very different singular nouns. They occur in such different contexts that they are unlikely to be confused, but one may be surprising to people who do not know it.
- The more common noun is axe - a large cutting tool used to cut down trees, swung with both hands, and like the one-handed hatchet in general form. The plural is pronounced 'AXE-iz'.
- In mathematics and mathematical subjects, axes is the plural of the noun axis. Being a Latin plural, it is pronounced 'axe-eez'. An axis is a straight line. The word can be used as a line through the centre of something (the 'axis of rotation'); as a line round which something is reflected (the 'axis of symmetry'); and as imaginary lines defining a space (the 'axis of reference'), particularly as the two lines used to measure the position of a point on a graph. There are many other special meanings which belong to subjects as varied as optics, geography, botany, engineering and astronomy.
For all of these, the correct plural form is axes.
For a note about the plural of axis, see -es in Latin.