The Circle organizes all the key signatures by fifths or fourths, starting from C Major
(whose key signature has no sharps or flats). The circle goes clockwise by intervals of 5 or counter-clockwise by intervals of 4. The key signature on the outside of the circle is the major key signature. The key signature on the inside of the circle is the minor key signature. The minor keys are listed together with their relative major (major/minor keys that have the same key signature.)

If you are interested in composition, The Circle of Fifths is an excellent tool for song structure. For any piece of music to be interesting, it must modulate between keys, flitting in and out of the primary key signature into related key signatures. The Circle of Fifths keeps the composer grounded in structure, as the modulation keys used must be kept close to the primary key. For instance, a piece in the key of C can easily modulate in and out of the keys of A minor and G Major, but would be awkward trying to modulate into A-flat Major.

Modulation can also occur quite nicely by fifths. Therefore if a composer is in C Major and would like to somehow get into B Major, this could be accomplished by traveling through the keys of G to D to A to E finally to B.