When a woman says she wants a man who is mature, she is most likely talking about emotional maturity. A man who is mature emotionally knows how to handle the stressful situations that can come up in a relationship. It can be difficult to tell if a guy is mature in an emotional way when you do not really know him that well. Here are a few things to look for that can point to emotional maturity.
Who are the people he considers his closest friends? A common saying is that you can tell all you need to know about a person by looking at his friends and the people he chooses to spend his free-time with. Are they people of integrity? Are they positive people doing positive things with their lives, or are they bums that sit on the couch all week playing video games and ordering in pizza? If his friends are negative influences, chances are he is either completely okay with that, or he is just like them, both of which are bad and are flashing signs that he is not emotionally mature.
Does he remain calm about matters that come up at work? Even if he has the worst job in the world, if he is emotionally mature, he will be able to handle the tough times and situations that occur in a mature way. Complaining about work every single day is probably a sign that he is not emotionally mature. Sure, it is okay to vent about work every now and then, but there is a fine-line between venting and just being immature about it.
How does he treat those closest to him? Is he really sweet to you but then turns around and yells at his mother over nothing? If so, do not be fooled. This is the type of guy who is putting on a front for you, but will end up treating you the exact way he is treating his mom eventually. Look at how he interacts with his close family and that will reveal a lot about his emotional maturity.