Let us have a look at the basic five shapes of major chords - those of the five CAGED Chords:
C major, A major, G major, E major and D major. It must be noted here that some strings utilize all six strings, while some are played using only the lower few strings so as to keep the root note as the bass note.
It will be obvious on observation that the bass note for all these shapes in the root note of that chord. For example, D major is chord (triad) of the notes D, F# and A, with the D note as the bass / note. If, now, we play the D major chord using the 5th string open - i.e. as x00232 instead of xx0232, thus incorporating the A note above, it still remains D major, though the bass note now becomes A, making it the 2nd inversion of D major play in open position.
These are the five primary chord shapes are shifted up and down and modified or some notes are added to these shapes producing all other chords. Some notes, at times are removed to produce them.
The basic theory behind movable chord shapes, as discussed briefly earlier, is that a chord is formed of some notes. A shape alters the effective length of the each string in a particular way. This preserves the frequency ratio between the notes played by that shape in any position - thus preserving the nature of the chord - major, minor, added, etc.
If we play a chord using that shape, the root note (and hence the pitch and name) of that chord is determined by the note that occupies the root position of these shapes - i.e. the note played on the bass note playing string of the basic shape. Hence, a D major chord shape is shifted down by two frets from open position and hence played at the 2nd position, will be E major (E major - second position - xx2452) as the root note, which lies at fret zero (open position - D note) is moved down 2 frets to the 2nd position (E note).
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