burden, noun (Middle English).
This is a musical term which does not have a literary meaning in the late medieval period. The word means a low-pitched accompaniment in a song (q.v. MED burden). OED records the word as referring to the chorus of a song from the late sixteenth century onwards.
burden, noun (Modern English).
In Modern English burden is used to refer to the repeated section of a carol, being the set of lines which begin the carol and are repeated after each verse.