I'd agree it's a pretty broad and hard to define topic. When it comes to maturity and respecting people though, I think there is at least one aspect that is important to recognize. Everyone is a complex person with deep thoughts, their own motivations, and they are perceptive of all sorts of things that they will not outwardly ever show. There are times when it is very tempting to label someone as "clueless" or "stupid" or just not the complex and intelligent person they actually are. There was a much younger version of me who had sort of drifted away from a friend. We were never great friends or anything, and I thought this person was a bit aloof and clueless about me, and I felt like a bit of an outsider on their particular circle, so I seriously thought they would have no idea I was even drifting. Much later I found out that that person had perceived everything going through my head, and it made me really re-evaluate the way I looked at people.
So, respect is, at least in part, keeping in mind that people are as capable of intelligent thought process as you are? That would mean that whenever people decide on something that you might find silly, ignorant or even dangerous, they do, in fact, have a certain base for that kind of thinking - and maybe, your perception of the decision is not entirely correct.