I can show you how it can help you find what chords are allowed in your songs when you are songwriting.

Take C for example. In the key of C, the tonic chord (chord of the key) is C, of course. Any of the five chords touching the C pizza slice are your allowed chords in your song, to put it simply.
Another way to figure out what chords may be used is to count the tonic chord of your key as 1 and count upwards until you get to 4 and 5. In the key of C, tonic is C, which is also 1. F is 4 and is called the pre-dominant, because it precedes the dominant. 5 is G and is the dominant. 6 is always your relative minor to any major key. In this case, it is Aminor. That means any inner slice of your circle of fifths pizza is the relative minor of the chord above it.
So if this makes any sense, I'll address C major:
1 = C
2 = d
3 = e
4 = F
5 = G
6 = a
I'm not going to address the 7 chord at this time, because it sounds like the 5 chord, except it is diminished.
I'll address aminor now:
1 = a
3 = C
4 = d
5 = e
6 = F
7 = G
I left out the 2 chord again, because it is a diminished chord. Not that Bdim isn't a good chord to use, but its really late and I want to finish my thoughts.
Once you get back to 8, it is the same thing as 1 again. 8 notes is a whole octave, right? ;) So this covers all the normal chords for a given key. Any key works with the circle, or just counting your numbers and alphabet if a circle isn't handy. The image I used I just googled.
Now, I've mentioned before that your 4 and 5 are called the pre-dominant and dominant chords. These three chords (with their relative minors) make up a majority of the music we hear today.
I want to talk about how to create these chords and sequence them into music, but I figured I needed to touch this first in case I'll be using terms or ideas that might be foreign to some of you. Right now I'm super tired from being up all day and then working an 8 hour shift, and I need to get some sleep (haha almost 3AM). If you have questions or if I messed up on a rule, feel free to post about it and I'll do my best to correct it and I'll use sleep deprivation as my excuse.