Let's break down a major key...

In the key of G major the notes are

G, A, B, C, D, E, F#, (G)

Then we built a triad chords from these notes taking a root, a third and a fifth note.

G - B - D

A - C - E

B - D - F#

C - E - G

D - F# - A

E - G - B

F# - A - C

Now let's analyze the intervals of each triad

G - B - D

is a root, a major third (four half-steps) and a perfect fifth (seven half-steps from a root). There is a major third interval, this makes a chord major, G major in this case.

A - C - E

is a root, a minor third (three half-steps) and a perfect fifth. There is a minor third interval, which makes a chord minor, Am in this case.

B - D - F#

is a root, a minor third and perfect fifth. Again a minor third interval. The chord is a minor, Bm.

C - E - G

is a root, a major third and perfect fifth. This time a major third interval. The chord is a major, C.

D - F# - A

is a root, a major third and perfect fifth. Again a major third interval. The chord is a major, D.

E - G - B

is a root, a minor third and perfect fifth. Again a minor third interval. The chord is a minor, Em.

F# - A - C

is a root, a minor third and diminished fifth (six half-steps from root). The chord is a diminished, F#°.

In general

- all the triad chords with a root - [u]a major third[/u] - perfect fifth are major chords.

- all the triad chords with a root - [u]a minor third[/u] - perfect fifth are minor chords.

The major key triad chord formula is always

major - minor - minor - major - major - minor - dim

regardless of what key we are in.

In G major this is G - Am - Bm - C - D - Em - F#°.

The chord degrees are typically marked using a roman numerals, so, that major chords are marked with a UPPERCASE letters and minor chords with a lowercase.

Then the general major key chord formula is

I - ii - iii - IV - V - vi - vii°.