When you're busy, you have things to do. You're occupied and probably not bored.
This word always means there's some kind of activity. When a phone line is busy, you can't get your call through. If you find the bathroom is busy, you'll have to wait it's free. When a supervisor is around, employees need to look busy. A busy intersection is loaded with traffic. If you're too busy playing basketball to finish your homework, your grades might suffer. It's good to be busy, but when people are too busy, they get stressed out.