> famous quote from Plautus

The quote from Plautus appears to be lupus est homo homini, which is much easier to parse. There's a verb and everything. (I didn't know that; I just looked it up.)

> I don't know how to properly translate dative to english, something like "to give".

Yes, the word literally means "giving [case]", but the grammatical concept in English is generally called "indirect object". English mostly doesn't have cases, so supplemental arguments to verbs tend to be marked by associated prepositions, making them "indirect".

When talking about Latin specifically or languages with noun case in general, it is normal in English to refer to the "dative case"; you don't really need to translate it.

I assume the case was named after the action of giving because giving is a very common action that necessarily involves three things. (Giver, gift, and recipient.) The name tells you what it means by example: "if a gift is given, the dative case is the one you'd use for the recipient".