To improvise means to make something up on the spot, or figure it out as you go. "Our boss decided to improvise his speech at our company meeting and when he started going off-topic, everyone could tell he hadn't prepared in advance."
Improvise comes from the Latin word improvisus, meaning "unforeseen, unexpected." Think about when something unexpected happens to you — you have no choice but to react in the moment, or improvise. Another meaning for improvise refers to acting onstage without a script. When actors improvise scenes for an audience, they create funny situations as they go, without having anything pre-planned. The Second City theater in Chicago made this type of comedy famous, with many well-known alumni like Tina Fey and Stephen Colbert.