What are third orders in the Catholic Church?

Third Orders are, in general, lay members of religious orders - men and women who do not necessarily live in community and yet can claim to wear the habit and participate in the good works of the order. The Third Orders can each be divided into (a) regulars - living in convents or monasteries, and (b) seculars - living in the world. Of these the first take vows, the latter can only make a solemn promise (except that Carmelite Tertiaries apparently take some sort of vows of obedience and chastity.)