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The two kinds of key signatures are major and minor.
Diatonic key signatures result from the diatonic scales. There are 15 diatonic scales and each of them have a key signature which corresponds to each scale. There is a circle of fifths which shows the system on how to come across each and every diatonic key signature and scale.
F major, B-flat major.
In the order of flats in key signatures, even if the melody skips the B-flat, the key would contain it, because there is no such key with only an E-flat.
It shows which notes in a piece are natural, sharp, or flat. Without a key signature, every single accidental would have to be written in instead.