The word "improvise" is closely tied to jazz music. Jazz musicians don't learn the exact notes to a song. Instead, they learn the general outline of a song and then make up parts of the music as they're playing.
People use the word "improvise" in a similar way to talk about doing things without a plan. For example, you can "improvise" for a presentation:
I couldn't open my PowerPoint presentation, so I just had to improvise.
To "improvise on" something means to start with a plan, structure, or recipe that's already been made, and then add things to it.