From my own personal experience (I'm part Zulu & I asked my mother this years ago) in a tribal situation, the placenta is eaten because of the nutrients it gives the mother.

The placenta isn't eaten if it covers the face of the baby, in which case it is dried and given to the child as an amulet (being born with a cowl is a sign of psychic ability). My great-grandmother ate my grandmother's placenta, my mother's placenta was dried and given to her (we have no idea what happened to it before mum left South Africa in her 20s but we know it never made it out of SA).