A Chord Progression is a sequence of chords that is repeated to make a song.
A Diatonic Chord Progression is a sequence of chords that belong to the key. In Diatonic Chord progressions there are no chords from any other keys.
The only chords used in a diatonic chord progression come from the key in which the song is written.
Look at the common chord progressions.
Notice The 5 chord is usually followed by the 1 Chord.
5 goes to 1.
C D E F G A B C
1 2 3 4 5 6 7 8
C is 1
G is 5
Five moves to one.
This is also expressed using roman numerals
V--> I is a chord sequence, or a harmonic movement known as a Cadence.
A Cadence occurs only when moving from the Dominant chord, or the V of the key to the I chord of the key. Remember, in diatonic chord progressions only the V chord is a dominant chord.
In the Key of C that means the cadence occurs only when moving from G to C.
It works like this:
When we listen to a song, we start to get a sense for the key in which the song is written. Even if we don't know the exact key the song is in, we can still get a general feeling for the key. When we hear the V chord, then we expect to hear the I chord next. Even if we don’t understand music theory or even know what a Cadence is, we still expect V to move to I. This is largely because we have heard cadences used in many songs and we recognize the sound on an intuitive level.
These chord progressions are common because they are mostly derived from the cycle of 5ths.
The cycle of 5ths lists all of the possible cadences, or V-->I movements.
We like to hear the V-->I cadences, and so it makes sense that there are many songs that use these chord progressions.