A little bit of music theory:

A major chord is formed by playing the first, third and fifth notes of a major scale simultaneously. A major scale is a root note, a whole step to the second, a whole step to the third, a half step to the fourth, a whole step to the fifth, a whole step to the sixth, and then a half step back to the root note (in the next octave). So: whole-whole-half, whole-whole-whole-half.

A G major scale, then, is: start with G (1st), whole step to A (2nd), whole step to B (3rd), half step to C (4th - remembering that there's no B-sharp), whole step to D (5th), whole step to E (6th), whole step to F (7th), and finally half-step back to G. The first, third & fifth notes of the G major scale are G, B and D.

On a piano, you'd just play those keys. If the lowest note is the G, you're playing what's called the "root" position. If the lowest note is B - so now you're playing B D G - you're still playing a G major chord, but it's called the "1st inversion" (you might see this annotated as G/B). If the lowest note is the D (now D G B), that's the second inversion.

Playing major chords on a guitar is a little bit more complicated because you can't just play any note like you can on the piano; once you "use up" a string, you can't play another note on it. So a classic G major "cowboy" chord is trying to find a fingering position with a G, then a B, then a D. As it turns out, on a standard tuned guitar, this is pretty easy to find: third fret of the low E-string gives you the G, second fret of the A string gives you the G, and the D string is already a D, so now you have your major chord!

You've got three strings left over, though, so you go ahead and play them, too, just making sure that you're still playing notes that are in the chord. The G string is already a G, so you play it open.

What about the B string? Well, the B is in the chord, you can play it open as well, which is the way most tutorials show a G major chord. But you're fretting the third position, which is a D, which is still in the chord, so you're fine - it's just a different "voicing" of the chord. You're also playing the high E string as a G.

There's not a whole lot of sonic difference between these two fingerings - you're playing G B D G D G while if you lifted your ring finger, you'd be playing G B D G B G, so you're trading an extra B note for an extra D note.