If you do something "to order", it means you only do what is required and when it is required. Improvisation is like that. You don't plan anything. You just do whatever comes to mind at the second that you have to do it.
It can be used when people say that they can't just do something spontaneously.
- Sarah, you're a really good singer, aren't you?
- Yes, I can sing. That's true.
- Sing us a song. Right now!
- Oh, no, I can't just do it to order. I would need to practice in advance.
Student or Learner