The most common use in drama when used to describe times in performance when a performer uses words not found in the text. (When the entire performance is spontaneous and unscripted it is called improvisation.) This occurs on the live stage, in films, on television and frequently in situations such as the conversations on talk-shows, news, podcasts etc.
Larry David's HBO series, Curb Your Enthusiasm, is often pointed to as an example of ad-lib drama. The show can also be said to use "retroscripting." The series also has created its own collection of words and phrases, as noted in the video shown here.
Less well known is its use as a direction in sheet music where "ad libitum" indicates that the performer or conductor has one of a variety of types of discretion with respect to a given passage.
Ad libitum is also used in psychology and biology to refer to the "free-feeding" weight of an animal when the animal eats as it wishes rather than its weight on a restricted diet.