Cyc, short for cyclorama, is a theater term for a large curtain positioned at the back of the stage.
The term has been adapted to film and television, where it refers usually to a curtain or wall that curves as it meets the floor to create the illusion of an endless floor with no horizon point. This is extremely useful for greenscreen work.
Technically this curved background is called an infinity cyc, but is now often in film and television circles when the term “cyc” is used.