According to Oxford dictionary “after” means following another period of time or behind and many others. So “after you” should be meant behind you or you should go later or let us go first then your turn. I'm actually confused?
It's a very widely used phrase, normally meaning "please, you go first, I will go after you."
A typical example would be if two people arrive at a door at the same time. One of them, being polite, might say "After you." The other person might then walk through, saying "Thank you".
Or, also being polite, might say "No, after you, I insist", and the first person walks through, saying "Thank you."
Other circumstances where you will hear this are when two people start speaking at the same time, or two people try to order from a bar at the same time.