This exercise is from the Theory Section on Chords - an introduction to Keys. Go there to learn more about the progression we are playing through here, and why.
Here we play out the chord triads we get from the C Major scale:
C Major scale: C - D - E - F - G - A - B - C
1 - 3 - 5 = Chord Triad
C - E - G = C Major
D - F - A = D Minor
E - G - B = E Minor
F - A - C = F Major
G - B - D = G Major
A - C - E = A Minor
B - D - F = B diminished
C - E - G = C Major
First we pick through these triads in ascending order. Playing this way means the root note for each triad is always played on the Low A string. The 3rd note is always played on the D string, and the 5th note is always played on the G string.
Excepting the B diminished chord for now, notice that the finger positions for each triad are very similar. In fact there are 2 main shapes. One shape for major triads, another for minor triads. The only difference between the two shapes is the note on the D string. That is the 3rd note and remember that the only difference between major and minor triads is that 3rd note!
You should learn and practice these 2 main triad shapes. They are a great way of quickly finding chords on the guitar! Practicing this exercise will help you learn these shapes. Later, when you understand more about chords you'll see why these little triads can be so useful. They are a nice alternative to playing standard E and A shape powerchords all the time, and can help you learn the location of notes on the fretboard easier.
As you play through these triads, say the note names (at least mentally). This will help you associate note locations quicker, and help you to further see the relationships between each chord!
After picking through the triads, we then fingerpick each chord. This allows us to hear how the chord triad notes sound when played together. Remember the triad is the foundation of each basic chord. This part of the exercise helps you see and hear the heart of each triad. It further helps you see what we are really doing in the next part of the exercise...
Next we play out the full open chords in a more typical format. We are still using the basic triads, but using more standard chord shapes. These give us a fuller sound and means we can strum more than just 3 strings to get each chord! You should be able to hear the chord progression is exactly the same (at heart), just fuller sounding!
So...from the C major scale (our key) we get a decent framework of chords. C major is a very common key, and so are the chords we get from it. Spend time and learn them if you haven't already...the chords here are a 'must know'.
The diminished chord is something we'll deal with later, just know for now that it is another type of triad (major or minor triads are more common, but not the only types of triad). Before we wander off into that territory make sure you understand your basic major and minor triads here!