I've wondered about the original meaning of this phrase. Latin, obviously, but what did it literally mean? Now I know.
abbrev. of AD LIBITUM advb. phr.
B. adj. Extemporized, improvised, spontaneous, unrehearsed. orig. U.S. Also as n., something spoken or played extempore (chiefly U.S.).
ad libitum, advb. phr.
At one's pleasure; to the full extent of one's wishes, as much as one desires. In Music opposed to obbligato.
Hence as adj.