"Grown up" means "adult". But the phrase "grown up" is usually used when you're talking to, or talking about, kids. For example, one of the most common questions to ask children is:
What do you want to be when you grow up?
This means "What kind of job do you want to have when you become an adult?"
The phrase "all grown up" sounds even more cute and child-like than "grown up". So if you said to a 19-year-old who you haven't seen in several years:
Look at you! You're all grown up!
it would probably be meant as a joke, because you're talking to him as if he were a child. The 19-year-old probably wouldn't think it was that funny.