It's about accepting and owning what's expected of you as an individual, autonomous, functioning member of society. Nothing more. Owning control of yourself.
Does this mean you have to get married, have children, and stop partying? No, not at all. Does it mean you take the initiative to pay your bills on-time and hold up your end of the bargain at work, at home, in your relationships, and society in general? Absolutely.
I'm in my mid-30s, and I did a lot of very hard partying clear into the twilight of my 20s well into my 30s. The money might have helped, but "growing up" made it a hell of a lot easier to enjoy those times simply because worry wasn't even on the radar knowing everything I could personally control was in check--because I made sure of it. Nobody else controls any aspect of my life that I myself can control.
And yes, with wife, child, and more micro-manageable responsibilities than I could have ever imagined when I was younger, I'm a hell of a happy person. Family, friends, gadgets, code, etc, etc.
What makes you grown-up isn't arbitrary; in the end, it's in fact a pretty clear line that transcends generations: Own. Your. Shit. But I'll leave the rest of the thread to conduct the typical older/younger generational ad hominems.