This nomenclature stems from the music: Most contra dance tunes (as written) have two parts (A and B), each 8 measures long, and each fitting one part of the dance. The A and B parts are each played twice in a row, hence, A1, A2, B1, B2.
This terminology originates from music: Most contra dances have two sections (A and B), each eight measures long, and each section corresponds to a distinct dance part. These sections are played twice consecutively, resulting in the notation A1, A2, B1, B2.