To extemporize is to speak or perform without preparation. Essentially, it's improvising. 

This skill is invaluable for speakers who need to adapt swiftly to the unexpected, whether answering questions or responding to a change in topic.

A CEO at a press conference might extemporize an answer when asked an unforeseen question. 

A substitute teacher might improvise a lesson when the planned materials are unavailable.

Extemporizing effectively requires a deep understanding of the subject and the ability to think on your feet. 

It showcases confidence and flexibility, traits that are highly admired in public speakers.

If you're a member of Toastmasters, you're familiar with “table topics”—one-to-two-minute off-the-cuff speeches that challenge you to invent a short speech on the spot.

Practicing extemporization will improve your ability to communicate under pressure. 

The more you practice, the more natural it will become. 

And if that sounds daunting, remember that in the average conversation, none of us has any idea what we're going to say five seconds into the future. We all extemporize every day!