The circle of fifths or circle of fourths, depending which way you want to go around the circle, is not just a mnemonic device--it is a rather peculiar phenomena having to do with the relationship of the keys to one another--

The most reasonable way to think about it is like this-- In every key, there is a tonic chord say "C", and a Dominant chord, say "G7"--(in fact, many songs just whack back and forth between tonic and dominant chords til the cows come home0

Now, if you take the Tonic chord, C and make it a C7, it become the dominant chord in for the key of F--F7 is the dominant in Bb--Bb7 in Eb until you have gone all the way around through all 12 keys--

There is a real, scientific reason that there is such a strong relationship between the tonic and the dominant, and that they sound right, alternating like they do in our western (diatonic) music, but I am to tired to explain it, and when you hear the ezplanation, you will understand what makes me so tired--

There are cultures where they don't bounce back and forth between Tonic and Dominant harmonies and stay on one chord, and that music is called monophony or sometimes *monotony*, which should give you a clue as to why we in the west have traditionally preferred to bounce a round a little--

The thing to remember is that when you move through the circle of 4th/5th, you are changing keys, and the reason is to avoid monotony--