The idea of the Circle of Fifths is essentially this: the interval of a fifth is important in Functional Harmony. It is important because it is the interval between the root notes of the Tonic (I) and Dominant (V) chords.

I (one) --> V (five) --> I (one)

This simple chord progression is the backbone of Functional Harmony. So it's valuable to know what the 5th of any particular tone is and therefore what it's chord is. Like this:

G (V) --> C (I)
C (V) --> F (I)
F (V) --> B-flat (I)

And so on. It's a very simple idea but very powerful and wide-ranging when you put it into practice. In order to do this you need to get used to systematically exploring the guitar to find every place you can put the notes (voices) together that form that chord progression in any and every given chord progression. And that is where it gets quite involved.

One example: finding lots of places on the D, G and B string to play the Dominant to Tonic motion G (V) --> C (I):

E |-----------------------------|
B |-0-1--3-5--3-1--8-8--12-13--|
G |-0-0--4-5--4-0--7-9--12-12--|
D |-0-2--5-5--5-2--9-10-12-14--|
A |------------------------------|
E |------------------------------|

For more on Functional Harmony (and where it fits into the overall set of concepts that form music theory) look at this:
http://www.guitartricks.com/tutorial.php?input=495