What follows is what I'm reading from Wikipedia, and my reactions. I hope it helps in clarifying what I'm confused about.
An interpretation is an assignment of meaning to the symbols of a formal language
1) So it's just semantics of formal languages?
In these contexts an interpretation is a function that provides the extension of symbols and strings of symbols of an object language. For example, an interpretation function could take the predicate T (for "tall") and assign it the extension {a} (for "Abraham Lincoln"). Note that all our interpretation does is assign the extension {a} to the non-logical constant T, and does not make a claim about whether T is to stand for tall and 'a' for Abraham Lincoln. Nor does logical interpretation have anything to say about logical connectives like 'and', 'or' and 'not'. Though we may take these symbols to stand for certain things or concepts, this is not determined by the interpretation function.
2) Oh, so what makes it special is that it maps a symbol in the language to other symbols in the language without concern for what they "mean" outside the language?
A formal language W can be defined with the alphabet A = {u, v}, and with a word being in W if it begins with u and is composed solely of the symbols u and v... A possible interpretation of W could assign the decimal digit '1' to u and '0' to v. Then uvu would denote 101 under this interpretation of W.
3) Okay, so it actually maps symbols in the language to symbols outside the language.
Now I'm confused about what an interpretation actually means, and how the second quote relates to the third quote in a coherent manner.