What a good question..
I think, for me, it is about different things externally and internally coming together in a sustainable way. No one is perfect, and people will gain/lose features here and there.. but if, overall, the components of these two can be maintained regularly by the person, I consider them an adult. And it's fluid.. people can revert, and regress into childish behaviors even though they were totally acting like competent adults before.
External factors: Age (sorry, even if you're the smartest 14 year old in the world, you're still 14), being self-sufficient financially (i.e. if your parents are still paying your bills and you aren't just 'hey its cheaper if we stay on the family plan so I'll shoot you money' doing that thing but actually just getting your parents to pay for you, you aren't stable), being able to develop and maintain a career path of some sort (even if that is 'I'm working at this coffee shop/staying in school until I figure out what to do with my life' that's still something.. if you're playing video games all day and not gaining anything new in return even if it's just money you aren't working like an adult) .. Stuff like that. It's hard to pinpoint outside of those things, because really culture varies.. people in NYC all their lives may never learn to drive, but that's childish in Houston where a car is necessary.. or for my family doing your own taxes was a big deal, but others have always hired tax advisers, and for us working early was majorly pushed because we grew up poor vs people who have time to go to college and just focus on that... so it's hard to make a total list.. but those are some ideas of external factors.
But the bigger, heavier hand is the internal ones.. The external factors get beaten up all the time (40 year old once-successful-people have to move in with their parents again, or people seeking higher education have to sacrifice somewhere, etc.), but the internal ones should more than make up for the higher variety of external factors. They shouldn't spike up and down nearly as much, and they make the difference between adults and older persons acting like adults sometimes when it's convenient for them and just having the title through society standards.
Internal factors: A sense of responsibility for one's own actions, a sense of duty (like, even though that garbage-can-cleaning job sucks at work you still do it because unlike a kid you fulfill obligations even if no one is looking at you right away.. Or like, your mom isn't going to pay your phone bill, you don't call mom to bail you out of that mess when you bought nothing but fancy record players and forgot the bill was due.. vs someone asking mom for assistance during a genuinely hard time.. that sort of thing..), a tolerance for suffering (I find to be a big deal.. childish people get butt hurt, throw tantrums, start fights, lack total empathy for others, etc.. I always find young people tend to lack any tolerance to deal with the bad or negative things in life, and I always considered it a sign of adulthood to be able to brace one's self and weather through the storms life throws at you without completely collapsing the rest of one's life and obligations as a result)...
My personal thoughts on it closer to my heart?: An acknowledgement of children and young people and a sense of duty to help them.. I feel like if you're still in the "I'm in this all for me" game and you have zero desire to acknowledge the younger generations and give something to them it's because you never grew up and created something worth giving..
Reflection into one's self.. being able to actively seek criticism, challenge one's own beliefs, and ask harder and more uncomfortable questions are signs of maturity and adulthood.. I think more childish people want to use defense mechanisms to get away from icky bad feelings or ideas like 'you've been wrong your whole life' or 'turns out I am a neckbeard' or 'I play the victim all the time' etc.
Having something around you that commands respect. Teenagers accept explanations (begrudgingly but still they do) like "Because I said so" and such. Having logical, well thought out ideas, being proactive about plans (like the teenager that talks to their parents ahead of time about wanting to learn to drive because they're wanting to go to technical school vs just obeying and going to college and flunking out because they knew they didn't want to go be a lawyer like daddy), and interacting with adults in such a way as to integrate into them are huge signs of growing up and being in an adult mindset. There's a big big difference between teenagers and young people 'acting' instinctively and then going "Oopss.. sorry? I didn't think of that.." vs one that can see the bigger picture and put pieces together ahead of time. I tried to explain this to my younger sisters when I was growing up that I didn't just automatically get to the trust-level with my parents that I have due to age.. I commanded respect, and made people see me as an adult. I didn't ASK for a car, and I worked hard and bought one myself--I did ask for advice about buying one though. Both my sisters expected cars to be given to them somehow after I bought mine. They could have worked like I did, but they didn't. Little issues like that created a gap between me and them in my parents' eyes.