The circle of fifths is an intuitive method for determining the relationships among all of the tones and key signatures used in music. It offers composers a way to visualize how the tonic and fifth degrees of a scale are linked and is useful for creating chords, harmonizing melodies and deciding how to move music to different pitch centers. The circle of fifths is also useful for musicians since it provides a way to efficiently anticipate and understand harmonic progressions and scale relationships found throughout music.

This image shows the circle of fifiths with all the colors using what is in Abelton. This way you can color your tracks in such a way that you can easily do harmonic mixing.
So basically the Circle of fifths is an easy way to make chords and notes that sound good together with in any scale. You pick a root, or key. Lets say C major. The major notes are one either side. F and G. The minor notes and chords are then D A and E. The diminished is B.
All of these notes will sound good togeather. You can also use them for chord progression. Go from a C chord to a D minor to an E minor to an D minor then back to C. Other such great ideas can be found in the circle.
Working with the Fifths is also GREAT for mixing live. If you have a song in C Major then mix with in the circle to get a really nice mix. It will add worlds to your DJing.Just as beat matching is important so is Harmonic Mixing.
Here is a great website that will give you an Interactive Circle of Fifths to play with.
http://randscullard.com/CircleOfFifths/
This is just a basic run down of some ideas. There is a lot to know on the circle and it will help your music production and mixing immensely.