Plain English Meaning
How wide the circle is when an airplane turns. A steeper bank or a slower speed makes the circle smaller. A shallower bank or a faster speed makes it bigger.
Full Definition
The horizontal distance from the center of a turn to the airplane's flight path during that turn. For a given true airspeed, radius of turn decreases as the angle of bank increases; for a given bank angle, radius of turn increases as true airspeed increases.
Context Anchor
Seen when learning how bank angle and airspeed affect the space an airplane needs to complete a turn.
Derivation
Radius comes from the Latin radius, meaning the spoke of a wheel or the line from a center to the edge of a circle. A turning airplane traces part of a circle, so radius of turn is simply the distance from the center of that circle out to the airplane.