to think and react quickly, esp. having good answers ready: When you’re called on in class, you have to be able to think on your feet.

think on (one's) feet To be able to think clearly in times of stress, especially when forming a solution to a pressing problem. Thank goodness you were able to think on your feet and find another way to stop the pipe from leaking.

to make a quick decision or give an answer quickly: I'd never heard about the company before, so I had to think on my feet.