Classy is not about clothes, makeup, hairstyles, accessories. It is not about being posh, or wealthy.
A classy girl is kind, gentle, sweet, empathetic, caring. She is giving, loving... she is a good person. She is polite. She has good manners and is a very pleasant person to know. She is a good friend.
Bruce is a classy fellow, he always sends such thoughtful messages.
Jill thinks she is classy but she is only fooling herself. There is nothing classy about passing out drunk on a wall.