A B Major chord contains the notes B, F#, D#. It is built from the major formula 1 - 3 - 5, with B as the root.
Why is there no open B major chord?
The open strings simply don't line up with B major's notes in a way that produces a playable shape low on the neck. Instead, guitarists take the A major shape and move it up two frets, adding an index barre — which is why B major arrives after barre technique is underway.