He's getting better all the time.
What does it mean by "getting better"? health? or?
It means he's improving. It could have something to do with his health, but there's no way to know because there isn't any context. It's an isolated sentence. He might be getting better at playing tennis or golf. He might be getting better, and soon he'll be leaving the hospital.
The expression "get better" and the verb "improve" can be used in many contexts.