Oh what a lovely term. A term certainly deserving of quotation marks. "Emotionally mature", The companion of "politically correct". However unlike its companion, the term doesn't mean the same as the sum of its parts.
Someone who has grown and progressed on an emotional level knows that the reason to leave quietly after being fired is because by making a fuss, it's a complete waste of emotional expression that results in you feeling like a five year old throwing a tantrum. Throwing a tantrum is far more emotionally satisfying when done alone in the car five minutes after quietly walking out of the workplace. The "emotionally mature" person however leaves quietly because they don't want to cause a "scene".
A person who has learned about their emotions, their triggers and effects, knows how to avoid cheating on their significant other. Though as humans are to do, when they do fail and cheat, they know it's too late for emotional control, and it's time to do the right thing according to their own set of morals. Not because it's the "right" thing to do, as the "emotionally mature" person would put it.
Get two "emotionally mature" people together to share a few meals and you'll end up having a few meals where there is always one piece of food left sitting on the plate, begging to be eaten by anyone. Asking "Are you going to eat that?" is not only polite, but good sense. Hopefully you're not asking the "emotionally mature" person as you will only ever receive an honest and sincere response if they genuinely don't want it.
Breaking up however, is something else entirely. Without elaborating on such a large and already heavily noded topic, chances are that if you have managed to separate your emotions from your actions enough to not break down, doing the "emotionally mature" thing is probably one of the few things you can still do that don't involve completely losing it.
As far as I can tell, being "emotionally mature" is rather more like being emotionally detached. Being genuinely emotionally mature is rather like attaining enlightenment; Probably impossible to achieve in one lifetime, a quality we envision only the wisest of people have, yet more likely that no one actually does. If anyone does have it, they probably aren't telling anyone or writing a book on it.
As unobtainable as it seems, I still feel it's something worth working towards, even if I never get it. I know it's all just some concept attached to a set of arbitrary words, no doubt all an illusion, but I still think it's worth it to try. Besides, when all else fails, you can at least try to be "emotionally mature", it's not perfect, but it's far better than grabbing hold of some poor person by the jaw and bringing a nearby sharp or blunt object quickly towards their head while screaming various nonsensical obscenities in the form of a question. Not to mention that sometimes, just sometimes, what you do afterwards involving spray paint, super-glue and used condoms is actually a healthy emotional expression.