I found a very short sentence on tatoeba.org. All it says is, "给你。"
That literally means "Give you," but what does it really mean? My best guess is that I could say it as I give something to you, kind of like, "Here you go."
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Your guess is correct. You use it when you hand over or give something. You can translate it as "there you are, here you are, here you go".
For example a teacher might say it while handing out some study material. A student of course should use 给您 when handing in his exam papers.
You can also add what you are giving. For example 给你一本书.
Yes it means "here you go". This certainly confused me when I arrived in China. (To be fair, the English "here you go" doesn't make any literal sense either.)
Directly translated, 给你 indeed means "give you". However in English, when someone gives you something, we usually expect it to be a gift. When using 给你, it doesn't necessarily mean a gift: it might do (e.g. in 给你个礼物) but not always.
When interacting with a shopkeeper, 给你 doesn't mean a gift.
This is a normal thing to say when giving a 100 yuan note to a shopkeeper. It's not a gift: it counts towards the payment of something, and the shopkeeper will still give you change. It's a good way to highlight how you know it's 100 yuan you have given them [so they can't later claim you gave them a 50 yuan note].
This is the version of "give" which implies it's a gift. Thanks for the 100 yuan.