Complex sentence: Most of the work that Burleigh did for Dvořák was copy work, transferring the manuscript of Dvořák's 9th symphony for the parts for various instruments.
Split into simpler sentences: Most of the work that Burleigh did for Dvořák was copy work. That is, Burleigh was the man who took the manuscript copy of Dvořák's 9th symphony, and copied out the parts for various instruments.