I'm wondering if it's because it has stem cells in it that can be used for health. This from Wikipedia:
The umbilical
cord lining is a good source of mesenchymal and epithelial stem cells. Umbilical cord
mesenchymal stem cells (UC-MSC) have been used clinically to treat osteoarthritis, autoimmune diseases, and multiple other conditions. Their advantages include a better harvesting, and multiplication, and immunosuppressive properties that define their potential for use in transplantations. Their use would also overcome the ethical objections raised by the use of
embryonic stem cells.