In a legal sense, we rely on biology. And in a technical sense, it's all about age. Since biology varies and physical maturity arrives at different times, this is somewhat poorly defined, especially in days when puberty comes earlier, but expectation to "grow up" is pushed later. We do know that certain markers for development occur near certain ages. But again, those markers are not stable and are being pushed earlier. I was reading the average age for puberty is now 9 years old.
In a more personal sense we often refer to emotional maturity. There are many definitions for what that means, however. This differs by culture, and by personal perspectives.
After years of observation and research, the simplest and, I think, most universal answer I have, is this:
Being a man means reaching a level of maturity high enough to take responsibility for your own life, and sometimes others.
This responsibility doesn't always mean financial responsibility or responsibility as head of a household. Sometimes this is as simple as being aware of self and others enough to accept the wisdom around us and act on it. Other times this means providing wisdom for others. This kind of maturity transcends disability and sometimes age.