1. Carried out or performed with little or no preparation; impromptu: an extemporaneous piano recital.
2. Prepared in advance but delivered without notes or text: an extemporaneous speech.
3. Skilled at or given to unrehearsed speech or performance: an accomplished extemporaneous speaker.
4. Provided, made, or adapted as an expedient; makeshift: an extemporaneous policy decision.

Synonyms: These adjectives mean spoken, performed, done, or composed with little or no preparation or forethought. Extemporaneous, extemporary, and extempore most often apply to discourse that is delivered without the assistance of a written text, though it may have been planned in advance: an extemporaneous address; an extemporary lecture; an extempore skit.
Impromptu even more strongly suggests happening on the spur of the moment: an impromptu dinner.
Offhand implies not only spontaneity but also a casual or even cavalier manner: an offhand remark.
What is unrehearsed is said or done without rehearsal or practice though not necessarily without forethought: a few unrehearsed comments.
Unpremeditated implies impulsiveness prompted by strong feeling: asked an unpremeditated question.
Something that is ad-lib is spontaneous and improvised and therefore not part of a prepared script or score: an ad-lib joke.