Recently a colleague of mind asked how I would explain inversion/eversion and supination/pronation. Below is my response:
In short, inversion/eversion are frontal plane motions of the ankle, whereas pronation/supination are triplanar motions of the foot/ankle complex. Inversion/eversion are components of supination/pronation. Inversion (i.e. - inversion ankle sprains) is often used interchangeably with supination, as is eversion with pronation, but they aren't exactly the same. So to answer your question:
Inversion occurs at the hindfoot (heel) as the calcaneous/heel moves in the direction that the bottom of your foot faces inward. When this happens in excess, an inversion sprain and/or an injury somewhere up the chain is likely to occur.
Eversion also occurs at the hindfoot, but instead of the heel facing inwards, it faces outward. And like with inversion, an injury may occur with excessive movement and/or stress in this direction.
The thing is, these motions rarely, if ever, occur in isolation so the terms pronation/supination may be more applicable when discuss closed kinetic chain movement(s) at the foot/ankle.
Supination is made up of inversion of the hindfoot, adduction of the forefoot, and plantarflexion of the talocrural (ankle) regions.
Pronation is made up of eversion of the hindfoot, abduction of the forefoot, and dorsiflexion of the talocrural (ankle) regions.
Remember, pronation and supination are necessary motions for proper foot/ankle function, as well as closed kinetic chain mechanics. But they must occur at the appropriate times and at the appropriate degrees to ensure sound movement. Pronation is necessary for force absorbtion, while supination is necessary for force production.