Extemporaneous means spoken without preparation. The orator's performance was impressive, but we did not realize the depth of his talent until we learned that his speech was extemporaneous.
Some politicians are so skilled that even their prepared remarks have an extemporaneous quality. As opposed to policy debates where teams know the resolution in advance, extemporaneous debates are judged on style and nimble argumentation, as the participants receive the resolution minutes before debating begins. Extemporaneous comes from the Latin phrase ex tempore, literally meaning "out of time." The words in this family (extemporary, extemporaneously, extemporize, etc.) almost always refer to speaking or composing something on the spot — without time or enough preparation.