Complex sentence: The end of the pigtail is stripped and fusion spliced to a single fiber of a multi-fiber trunk to break out the multi-fiber cable into its component fibers for connection to the end equipment.
Split into simpler sentences: The end of the pigtail is stripped and fusion spliced to a single fiber of a multi-fiber trunk. Splicing of pigtails to each fiber in the trunk "breaks out" the multi-fiber cable into its component fibers for connection to the end equipment.