The Playgoer: The Full-Price "Preview":
The term is becoming downright anachronistic. On the Broadway of old--as evident in old movies from "42nd Street" to "The Producers" plays truly "opened"--i.e. premiered--on "Opening Night" (after perhaps some open/invited dress rehearsals). Then by the 1960s, tickets would be available--at a DISCOUNT--for two or three pre-opening performances as a warm-up.
Off Broadway this didn't matter much I suppose since you were lucky to get the NY Times critic to come at all, let alone to your first night. But now, not only does everyone do "previews" but when the run is already limited and you control the schedule, some nonprofit companies have specialized in delaying official "opening" as long as possible so that if reviews are bad, the show will already be closing and thus unaffected. In other words, the preview period has been longer than the official "run." (I think Joe Papp pioneered that practice to get around critics.)