A lot of times when people ask this, they mean man (as different from woman) or man (in how he relates to women). Many of the same things that separate the men from the boys are the same things, however, that separate the women from the girls. It's too easy to come up with emotionally dead he-men who have no capacity for forgiveness or error.
Boys, in many cultures, become men when they pass through a rite of passage. Alternatively, those rites recognize that they've already become men. In most modern Western cultures, we have no similar things and many men wander around in some vague mixture of the two forever. Turning 21 is usually celebrated, at least, and marriage is a weak substitute.