What is the basis for determining a feature must be categorized or not?

what is the basis for determining a feature must be categorized or not?
In course ‘Kaggle Fundamentals’, why do we have to categorized ‘Age’ feature? and how to decide the size of bin?
example: kid is 7-10, adult is 20-40. Maybe in this case, it is easy to categorized age. But in case of the price. How to determine the bin?

My english is not good enough. Sorry for that guys, i have tried my best to improve my second language