Definition
The minimum descent altitude (MDA) and visibility values published on an instrument approach chart that allow a pilot to maneuver visually around the airport at low altitude to land on a runway not aligned with the instrument approach being flown.
Plain English
The lowest altitude and the minimum visibility a pilot is allowed to use when, after flying an instrument approach, they need to circle the airport visually to line up with a different runway before landing.
Context Anchor
Seen on instrument approach charts when the pilot may need to land on a runway that is not lined up for a straight-in landing from that approach.
Derivation
Circling here keeps its everyday meaning -- flying a curved path around something. Minimums is aviation shorthand for the lowest altitude and visibility legally usable on an approach. Together they describe the lowest values you may use while flying around the airport to land.
Why Pilots Care
Provides the minimum safe altitude and visibility needed to avoid obstacles while circling, directly affecting the decision to continue or execute a missed approach.
Intuition Check
Circling does not mean you must fly a neat circle around the airport. It means you are keeping the runway area in sight while maneuvering visually, and the published minimums are required limits, not suggestions.
Example Sentence 1
The wind favored Runway 14, so we flew the ILS to Runway 32 and used the circling minimums to maneuver and land the other way.
Example Sentence 2
Because the ceiling was 900 feet, the crew checked that they could meet the circling minimums before starting the approach.