The idea is to give the eye something continuous while everything else changes. A circular object cuts to another circular object; a hand moving left to right cuts to a car moving the same direction. The visual element persists across the edit, so a leap in time or place feels smooth rather than jarring.
The famous example is Kubrick's cut in 2001 from a bone tumbling through the air to an orbiting spacecraft — four million years crossed in a single frame, held together purely by shape and motion. Lawrence of Arabia's cut from a blown-out match to a desert sunrise works the same way.
There are variants worth distinguishing. A graphic match rhymes shape or composition. A match on action cuts mid-movement, with the motion completing in the second shot, and is the workhorse of invisible continuity editing. An audio match uses sound rather than image to bridge. All of them require planning at the shooting stage — you cannot invent the rhyme in the edit if you did not film it.