I mostly mean mental maturity in dating, as in how you act, respond, etc..
Most Helpful Girl
Mature people feel secure in their identity, don't feel threatened by other people's looks, success or wealth, etc., know and accept their own strengths and weaknesses, and are able to control their emotions, while still validating them and not avoiding them.1
Most Helpful Guy
There are two key things I look for in a mature person.
A - The ability to genuinely admit they were wrong. "You are right, and I was wrong." And I don't meant this in a low self-confidence, or mocking sort of way. This person genuinely means it, and says it with the intention of becoming a better person by admitting they were wrong in the first place. That shows you are not blinded by your ego.
B - The ability to adhere to symmetrical logic. Immature people judge other people, but they NEVER judge themselves.
"You see that girl over there? She's shallow as hell for saying I'm overweight and that she's not attracted to me. Never mind that I never date other fat girls, forget all that, she should like me for who I am on the inside."
A true, mature person can truly see themselves. They have true self-awareness, they can see all their good, and ESPECIALLY their bad.2