A useful way of exploring how a Major key (like C Major) sounds and feels is to wander around the "Diatonic Cycle of 4ths".
"Diatonic" means "within the key" — so here it means within the key of C Major.
"4ths" means a musical interval of a 4th:
C to F (C - D - E - F) is a diatonic 4th
F to B (F - G - A - B) is a diatonic 4th
B to E (E - F - G - A)is a diatonic 4th
"Cycle" in this case means a repeating pattern of "4ths".
In C Major, we learned the C Major Scale as Letters & Numbers:
Letter Names: C - D - E - F - G - A - B - C
Numbers: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 1
But in this Cycle of 4ths it would re-ordered as:
Letter Names: C - F - B - E - A - D - G - C
Numbers: 1 - 4 - 7 - 3 - 6 - 2 - 5 - 1
CYCLE OF 4THS: WITH 2-3-3
The cycle of 4ths in C Major, using the 2-3-3 format.
CYCLE OF 4THS: WANDERING
This the cycle of 4ths in C Major, wandering around the fretboard (breaking out of the 2-3-3 format.)
Also, the 2-3-3 format is useful for playing modes/scales, but not as user friendly when it come to adding other intervals (i.e. starting to add harmonic language)
CYCLE OF 4THS: ADD A 3RD
The cycle of 4ths in C Major — but with a Diatonic 3rd added above or below each note. We can refer to this 2-note combination as a "Diad".
A "Diad" is 2 notes, as opposed to a "Triad" meaning 3 notes.
A "Diad" is also just an interval (between two pitches), but it can help to think of it as a small chord too!
CYCLE OF 4THS: WANDERING WITH 3RDS
Wandering around the cycle of 4ths in C Major with a Diatonic 3rd added above or below each note.
CYCLE OF 4THS: ADD A 3RD + ADD A 5TH
The cycle of 4ths in C Major Diads — but with an Diatonic 5th added above or below each diad.
A "Triad" meaning 3 notes is commonly considered to be stacked 3rds (i.e. C - E - G, D - F - A, E - G - B, etc.), but you can also think of it as three pitches played together like C - F - G or C - D - G.
CYCLE OF 4THS: WANDERING WITH 3RDS AND 5THS
Wandering around the cycle of 4ths in C Major with a Diatonic 3rd and a Diatonic 5th added above or below each Diad.
On the guitar, 3-note chords are pretty nimble and easy to move around.