Other Uses of the Circle of Fifths
Key Signatures - You can also tell how many sharps and flats are there in a given key by looking at the Circle of Fifths. See illustration.
Transposition - The Circle of Fifths can also be used when transposing from a major key to a minor key or vice versa. To do this a smaller image of the Circle of Fifth is placed inside a larger image of the circle. Then the C of the smaller circle is aligned to the Eb of the larger circle. So now if a piece of music is in Ab you can see that when you transpose that it will be on the key of F. The upper case letters represent major keys, the lower case letters represent minor keys. See illustration here.
Chords - Another use for the Circle of Fifths is to determine chord patterns. The symbol used for this are I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor) and viio (diminished). On the Circle of Fifths, the numerals are arranged as follows starting from F then moving clockwise: IV, I, V, ii, vi, iii and viio. So for example a piece asks that you play a I-IV-V chord pattern, looking at the circle you can see that it corresponds to C - F - G. Now if you want to play it in another key, say for example on G, you then align the numeral I to G and you'll see that the I-IV-V chord pattern now corresponds to G - C - D. See illustration here.
Images from wikimedia.org, worshipacademy.com, bach.org and songweaver.com