What is the circle of fifth's in music?

The circle of fifths is a way of figuring out how many sharps/flats a key. Starting with C major, you go up a fifth and put a sharp on the seventh degree of the scale, which is F sharp - so the key of G major has one sharp.

This can be done by going up a fifth from G to D, in D major the F sharp (third degree) is already present and again you add a sharp to the seventh note, C-sharp, thus D major has two sharps. This goes all the way round to C-sharp major, with all notes made sharp.

You go down a fifth from C major to F major and lower the fourth degree, making the B a B flat, this F major has one flat. Again by going down a fifth from F is B flat and the fourth note is lowered so you lower the E to E flat, so B flat major has two flats. You keep going until you reach the key of C flat major, with all notes in the scale flat.