Here's a link to an article about eating one's own placenta after birth. Warning: plenty of ads on this site, including some that dance across the screen, as well as some pop-ups. If you don't want to deal with all that, here's a quote:
Basically, it is fine to consume the placenta -- and many traditional cultures advocate the use of the placenta for obvious reasons. The placenta is chock full of iron (lots of blood in there) and hormones, too. During pregnancy, many women develop anemia, a low iron and blood cell state, from a combination of the fetus preferentially getting iron and from dilution of red blood cells by increased fluid volume in Mom. Additionally, women experience a fairly sizable blood loss at delivery and this contributes to their need to increase iron in the post-partum period.
In Chinese medicine, dried placenta is used as a medicinal material, called 紫河车 Zi He Che. The traditional functions are to replenish Essence, nourish Blood, and benefit Lung Qi.
Kidney jing is derived from one's parents. When this is deficient, patients present with symptoms associated with Kidney yang, jing and blood deficiencies. Typical symptoms include immature development of the sexual organs, infertility in men and women, low sex drive, impotence, spermatorrhea, irregular menstruation, back and knees soreness and weakness, tinnitus, and dizziness. Zi He Che is the best choice to tonify jing, as it is the part of the body most directly involved with the development of a human being. -Chinese Medicinal Herbology and Pharmacology, p. 916
The picture at the top is of a placenta being cooked in preparation for drying, powdering and encapsulation. Here's the complete article, a really great step-by-step guide for those of you too squeamish to eat your own placenta over pasta.