Why is E major chord used in A minor relation?

A term for you--"functional tonality". Look at the "functional" part of the term. It's there because the way the notes are used have a function: primarily, to tonicise a particular pitch-cl (to set up a note as the "home" note). The middle note of the E major chord contains the leading note of the a minor scale. If it is sharpened to G#, there is a semitone between the leading note and the tonic (G#-A) as opposed to a tone (G-A). The semitone gives a stronger pull toward the tonic, thus increasing the sense of it being the "home" note.