Adulthood has many definitions depending on which context, i.e. sexual/emotional maturity, independence, etc.
I'm over 18, the (legal) adult age, but I've been emotionally mature since I was a little kid. I sorta had to grow up with no parents around. For this reason, I grew up a little faster than others and worked harder. Since I was a little kid, people have been always telling me I sound like an adult.
So, I guess being an adult is meeting all the criteria of maturity that have been universally accepted to define adulthood. One MIGHT think that what I said in the first few sentences of my rant would make me an adult. Contrarily, I'm sorta immature in other areas...lol.
A lot of people are adult sexually (i.e. what Ulti stated, lol) and legally, but still falter in the other criteria.
Scenario: A person goes on a shopping spree in spite of the fact he HAS to pay rent in a few days or he'll be evicted (financially immature). This would result in "asking Mom" (independently immature). Mom would then say "I don't have the money!" or whatever, then rant on about responsibility. He would then react to her statements with loud emotional outbursts about how Mom never helps him and how unfair life is (emotionally immature). Later that night, contemplating, he calls up a friend about his problem earlier. After talking for a bit, his friend suggests going out to a bar. He says yes, of course, spending his last few bucks drinking and God knows whatever else (lack of self-control). End rant... One may see a pattern or cycle going on here and what happens to the individual in my rant is anyone's guess.
So the point is: Legally and sexually you're an adult (that's a given), but you are lacking in the criteria to absolutely define yourself as mature enough be to be declared the IDEAL adult. This, however, is an old "system". The new "system" just states you have to be 18, curse, smoke something, have a kid or two, have sex, etc. Most kids are practically raised on this new system.