Plain English Meaning
To leave your planned route for a short while — usually to go around bad weather or another problem — and then either rejoin the route or follow a new one given by ATC.
Full Definition
To depart from the assigned or planned flight path, usually temporarily, in order to avoid hazardous weather, traffic, terrain, or other obstacles before returning to the original route or being assigned a new clearance.
Context Anchor
Seen in instrument flying when a pilot needs to avoid thunderstorms, heavy precipitation, or other unsafe weather along the planned route.
Derivation
From Latin deviare, meaning 'to turn off the road' (de- 'away from' + via 'way, road'). The use keeps the original sense exactly: turning away from the path you were on.