Also, when people talk about the key of the song, all of the chords in the song fall in that key's scale.
For example, a C major scale would be C D E F G A B C, you wouldn't find a B flat chord in a song that's in C major because B flat isn't in that scale.
If you want to get into a bit of theory, in major keys the 3rd note (E) and the 6th note (A), those chords you play as minor chords. This all goes back to classical music tendencies and has survived hundreds of years.
So for the chorus of The '59 Sound it goes C (The first note or root note), F (the 4th note), A minor (the minor 6th note), G (The 5th), then back to F, then back to C, F, Am, G and ends on C.
The reason that a lot of songs end in the 5-1 progression (from G to C or whatever notes are 5 and 1 in the key that youre playing in) is because that is the most desirable change in frequency to the human ear. It gives a sound of conclusion which is what our brain and ear like.
For more, just ask.