A fleshy, meaty looking chunk about as large as the last joint of your thumb was most likely a placenta. A placenta forms at the spot where a fetus attaches to the inside of the mother's uterus; it is sorta like the "plug" where the umbilical cord attaches (it's more complicated than that, but that's close enough). Normally, the doe eats the placentas, the umbilical cords, and the fetal membranes as she cleans the kits, but sometimes she may miss one or two, particularly if the babies get born rapidly.