OK, I'll try to explain it.
This chart is like hooked on phonics. It's the beginning of chord progressions. This is like the first day of the subject in a music theory class. Of course there are other types of music besides "Diatonic" (in the scale) which is why there is a name for it. So the most common example would be like in the key of A Minor (Am)
Am Bdim C Dm Em F G
Could also be
Am Bdim C Dm E F G
So I replaced the E minor chord with a E Major (E). Now in classical music theory we use a slightly different scale the harmonic minor to play melodies and this whole thing goes off into many variations some of which are based on Western Classical Music Theory and some of which that are not and are folk music based (are part of what we call music theory which is nothing more than a collection of notes that some culture used over and over).
So if you go into cycle of fourths / fifths and a lot of the more Jazz oriented application of that you get to where you can use any chord in any song as long as it's approached and resolved "correctly". To make a long story short what you have hear is like the times tables of chord progressions. There's a lot more to mathematics than times tables.
So no, that's not all there is to it but... it's a lot more than what most people know, just like most people don't know their times tables in math.
This along with the circle of fifths and understanding that (very simplified version of how it works) all of the minor and the diminished chord can be substituted with major chords instead would be way more theory than most people know.
So if you have a Do Re Mi "Diatonic" Scale for example C D E F G A B C (C major) and you make a melody with it, you can use the Chords C, Dm, Em, F, G, Am, B Ddim to harmonize it. On beats One and Three in time signature 4/4 you usually have a melody note that is a chord tone so if your harmonizing a melody you pick a chord that has the same note as the melody note on beats one and three. If I'm playing over a chord progresssion where I picked the Diatonic Chords in the key of C Major then I would make sure my melody had notes in common with the chords. Yes it can be (and often is) that simple in modern pop music. It's just not a "rule" because there are many cultures we an borrow from besides 17th century "Classical" music. Many! Hope that helps.
I've covered this stuff before and put up the same chart before and a pretty good explanation of how I see the relatinship between chords and scales here