The days of "lady" being defined by things like wearing little white gloves and a certain kind of hat are long gone; but I think the concept of some women being "ladies" is alive and well (although not universal, by any means).
I think it has to do with having a certain level of refinement, self-respect, dignity and graciousness toward other people. "Refinement" doesn't necessarily mean some artificial and unnatural kind of reserve - just having a line that wouldn't be crossed when it comes to being loud or crude. Graciousness has more to do with treating other people in a way that doesn't make them feel bad and that doesn't disregard their self-respect and dignity.
I think today's "lady" is strong, capable, and willing to speak up on behalf of herself and others. In fact, I think these things are part of what make up today's definition of a "lady" because they're also part of an ideal for both women and men.
The men's version of the person above is "gentlemen" (but, as with "lady", without some of the more superficial, old, behaviors or clothing accessories and accessories).
I think a lady has natural, easy, manners and dignity; and a good sense of humor as well (but doesn't laugh at other people or play practical jokes at the expense of others' dignity). I think ladies hope others will notice them for "who they are" , rather because they wear clothes that reveal more than some people consider is dignified. In other words, today's lady can be entirely fashionable and even casual (rather than wearing some 1800's or 1950's version of "ladylike clothes), but she draws the line on clothes that some would call "trashy" or else "tacky".
In short, I think a lady is a thoughtful, naturally kind-of-refined, person who respects herself and others; and who is naturally well mannered in her treatment of the world and others (even if those good manners are defined by today's standards).