Major chord construction - C Major triad

The C Major triad is made up using the standard formula for major triads. In this case the 1st 3rd and 5th notes from the major scale.

The notes in the C Major scale are

C D E F G A B C

Therefore taking the 1st 3rd and 5th notes from this scale gives the triad notes of C, E and G

Taking this one step further if you look at the first position C Major chord you have the following notes

5th String 3rd Fret = C
4th String 2nd Fret = E
3rd String open = G
2nd String 1st Fret = C
1st String open = E

So you can see that the open chord fingering doubles up on the C and the E notes but keeps within the triad note structure.