One meaning for "There you are" is something like "I found you" or "I see you." For example: You are looking for your friend at a party, and after walking inside the party for a while, you find him/her. So you say "There you are!" the moment you see him/her.

well you could give someone something, a drink or a sandwich for example - could be a lot of things and say this. Shopkeepers sometimes say this when they hand you your change. Sometimes people in the uk also say 'there you go'. I've heard it used to make a point. For example, you could be told about someone who was rude and say this to mean you are not surprised. Also, resignation, you could be having a bad day and perhaps you have just hear your train is late, 'well, there you are'. Of course it could literally mean that someone has just seen you. 'Oh there you are'. Hope this helps, good luck in your studies.