What do signatures mean?

I’m quite used to transposing music to where it fits my instrument, even though I know some people don’t approve of this. I think what is important to know when doing this is what character is implied by using a certain signature. Since I don’t have a copy of Mattheson’s Neueröffnetes Orchestre I looked for the quote and found this page that quotes Mattheson directly on what they mean. Here is a translation to English by Babelfish