Key Signatures tell us what notes are sharp or flat in a scale. When we say we are in the Key of F Major we are saying that we are using the notes of the F Major scale. The Key Signature for the Key of F Major would be one flat, because there is one flat in the F Major scale.
Any single Key Signature symbol will identify both a Major and (Natural) Minor scale, for example C Major and A (natural) Minor have the same Key Signature symbol.
Examples of Key Signatures: