Good day Sirs and Madams!
Could you please explain the meaning of these idioms and give some examples of proper usage of them.
Thank you very much in advance 
These expressions are primarily used in conversation when someone is handing/giving something to you. This is the sort of thing that a shop assistant would say to you as they handed you what you have just bought or a waiter would say to you when putting the dish you ordered at a restaurant on the table. They are expressions that are informal and friendly and are often phrased also as: There you are/Here you are.
Alan
I see. Thank you! And is there any differences between them? When should I use one or the other or are they equal?
To add to what I have already said, I would suggest that ‘There you go’ is just a little less direct than ‘Here you go’ but this is a small difference. When I say ‘Here you go’ I am being a little bit more friendly. In all honesty I am finding it difficult to show the distinction.
Alan
***** NOT A TEACHER *****
Hello, Gatherer:
I believe that “There you go!” (depending on how you say it) can also mean something like “That is a good way to think about the matter.”
I have made up a bad example, but maybe it will give you the idea.
Mother: Please go to the supermarket and buy me some potatoes.
Mona: Oh, Mother. I am busy learning English at English-test.net.
Mother: I really need the potatoes. Can’t you do this one little favor for your mother?
Mona: Do I have to?
Mother: No, you don’t, but …
Mona: OK! OK! I’ll go.
Mother: Thank you.
Mona: Maybe going to the market won’t be so bad. I will get a chance to get some exercise (I have been getting a little chubby recently) and – who knows? – I might even meet a cute boy at the market!
Mother: There you go!
James
Come to that, it can also be used to mean something along the lines of, “There is no more to be said on the matter.”
Thank you all very much for such interesting answers!