Hey Tim. Good question!

Well, the phrase "7 C major chords" refers to 7 chords of the C major scale

How is that?
In simple words, C major scale is this:
C - D - E = F - G - A - B = CThis scale as you can see has
7 notes.
If you want to build a chord out of this scale, it's built by taking
1st, 3rd and 5th note out of the scale.
In the case of C major scale, those notes are
C E and G. This chord (CEG) is know as
C major chord.
Now, if you create D dorian mode out of C major scale, simply by starting from D and finishing on D:
D - E = F - G - A - B = C - D
Now you have built completely different scale using the same notes. The scale is different because the spaces between the notes change place.
Now, let's create a chord out of this scale (mode). 1st note is D, 3rd note is F, and 5th note is A. These three notes played simultaneously create
Dm chord.
You can
repeat this procedure
for every note of the C major scale.
So, C major scale has
7 notes, starting from each note you create
7 scales, and each scale builds a chord, which creates
7 chords!