Being on the ball can also be used to mean the person is thinking ahead and quick to react.... like balancing on a ball and being ready for whichever way it may roll

机敏、反应快，能够随机应变并且反应正确、适度。可能来自杂技演员的踩球表演。

"On the ball" means that you are competent and attentive. If you are "on the ball" at your job, it means that you get your work done well and in good time. https://idioms.thefreedictionary.com/on+the+ball If you are interested in the history of the idiom, check this: https://www.phrases.org.uk/meanings/on-the-ball.html

There are several different ways you can use this expression. Some good examples here: https://idioms.thefreedictionary.com/on+the+ball

This means that someone is "Up to date" or possibly if they understand something quickly and accurately. It probably comes from a football context, where they may say 'someone is on the ball' when they control the ball during the game in a skilful way. I hope that helps!