A major scale has 7 different notes. (You might count 8 here, but the first and last notes are both C). In a C major scale these notes are C-D-E-F-G-A-B. We number these notes using Roman numerals, so we can talk about them regardless of key.
We can use the notes in this scale to build triads – chords using three notes. Some of these are major chords (written with uppercase Roman numerals) and some are minor (written with lowercase). The second, third, and sixth chords are always minor. The seventh chord is always diminished.
Diminished chords show up in jazz, but are rare in pop and rock. Normally it's replaced with the flattened seventh - A B♭ major instead of a B diminished. This sounds like a big change, but it's actually only changing the root note of the chord, and only by a semitone:
(The major scale is also known as the Ionian mode. The major scale with a flattened seventh is also known as the Mixolydian mode. That's not relevant to triads, but it will come up later. Sooner if you hang out with jazz people.)
The chords we saw above are in root position – which means the bottom note is the root of the chord. C major is built C-E-G, D minor is built D-F-A, etc. You could also build a C major chord starting on E: E-G-C. That's called the first inversion. The second inversion is built on a G, G-C-E:
An open chord spans a couple of octaves. That's great news for a singer-songwriter (one voice and one acoustic guitar), but not great with distorted electric guitars or larger ensembles. Your sound gets muddy if you're playing with others and everyone's using the same pitch range. But triads are narrower; they'll sound cleaner when played with distortion, and leave space for your bandmates. Maybe you'll play some rhythm close to the nut while your soloist wilds out at the 12th fret. Maybe your piano will sit around middle C, and you'll add some chords an octave higher.
This riff is a big jump with open chords, but really easy with triads. Compare the first repeat with the second. Both versions are changing between A and D major:
Pianists and jazz guitarists often use voice leading, which basically means "small changes sound smoother". An A and D major chord seem quite far apart (they're chord I and V in D major), but in bar 2 of the previous example we used the first inversion of the chords to keep them close together. Our bass note moved by a tone (E to F sharp), and our top note by a semitone (C sharp to D).
Voice leading like this is great when playing arpeggios and fingerpicked sections. Small changes to your fretting can change the chord dramatically.
You started with an open C chord. Later you learned the barre form at the 3rd fret. That was just the beginning! Now you know lots of C chords!
As a byproduct of learning triad positions, you'll also learn the positions of notes on the fretboard.
Bad news: there's a lot of shapes to learn. Good news: they come in groups. You can see all the shapes in the triad exercises but let's take a quick look at an example on the top 3 strings.
These will be tricky to play because we've kept the key the same between the inversions. In the exercises we've shifted the key for each inversion. The root position is built from an A shape.
First inversion is built from an E shape.
Second inversion is built from a D shape.