To "keep someone occupied" means to give them something to do for a period of time. You keep people occupied so that they won't:
- get bored
- cause trouble
- notice something bad that you're doing
For example, in movies thieves will do something to keep a guard occupied while one of them breaks into a place and steals something.
Parents often need to give their kids something to keep the children occupied while the parents are cooking or doing work at home.
You can also "keep yourself occupied" if you have a long period of time with nothing to do, like when you're retired:
He's been keeping himself occupied with some housework and a little reading.