It is easy enough to tell people to "man up" or to become a man. Sometimes the speaker means that they want someone to fill some specific "man's role" -- whatever that is. Usually "man up" doesn't communicate much at all.
In some cultures "being a man" has a specific definition. It may be someone who has the right scars. Or, it may be someone who has killed a large game animals. In some places you are not a man until you have counted coup on an enemy on the battlefield. In other places, you are not a man until you have had sex or gone through an initiation ritual. Those are all benchmarks. They are acts or experiences that stand in as a proxy that is used to signal a measure of self knowledge.
So, what is it that makes the difference -- that makes a boy into a man? It is a measure of self knowledge and of taking ownership of one's self. It means not being oblivious and not hiding from yourself behind passivity, or silence, or food, or resentment, or any other method. It means taking mature ownership of yourself, your behavior, your feelings, and your goals.
Sure, the past exists. Things have happened, there are difficulties everyone caries with them. But at some point you take ownership of the present and the future and cease to be a reactor to events or a slave to destiny. Wallowing in the past is holding onto childhood. Clinging to powerlessness is clinging to infancy.
So, love yourself. Acknowledge yourself. Take ownership. Do not reject the past, make it an experience and a lesson learned, not a trap or a regret. Move into the present and find and move into yourself. Become what you are, become a man, that is what it really means.
If you find you don't like yourself, don't hide from the truth. Hiding doesn't change things. Take ownership and acknowledge yourself and then decide what you are going to choose for the future. If you can't love yourself, either grow up or change.
Anyway, that is what I had to say when asked what does it mean to be a man.