To 'think on your feet' means to react to events and circumstances quickly and without prior thought. Someone who can 'think on their feet' is adept at changing and responding to things. Similar in meaning to 'improvise' or 'make it up as you go along'. This idiomatic phrase is used as an adjective and has a very positive connotation.

1. My friend really put me on the spot when, totally out of the blue, he asked me to say a few words at his wedding. It's very hard to think on your feet when you're standing in front of so many people!
2. When the man collapsed in the middle of the street, I didn't have time to think about it I had to think on my feet.

1. I really didn't expect some of the questions I received in the job interview, but luckily I'm good at thinking on my feet.
2. This is a high-pressure, unpredictable job. We need someone with the ability to think on their feet.