Today, it generally means politeness. I think it's always nice to be polite to people. No woman in the US is treated as a "lady" in the classic 19th-Century sense of the word anymore. In other words, men are allowed to give casual gifts to a lady, whereas this was once considered a rude and scandalous thing to do to with ladies. Ladies today are allowed to walk the city streets alone without anyone automatically assuming that she must be a prostitute. Proper ladies are no longer escorted everywhere by a man standing on her left with her arm in his. Ladies today can do what they want and say what they want now, so we truly are equal in the social sense.
If we're talking about holding the door for someone or holding the umbrella for someone as they get out of the car, I would do that for a man or a lady. I supposed the only questionable act left today is rising whenever a lady leaves the table or sits down at the table. Most people don't really do this anymore either. Weddings are traditionally paid for by the bride's parents, but this is going away.