I had heard of this before, but I recently saw a story on CTV about it, where the midwife offering the service of encapsulating women's placentas after they give birth says that other mammals eat their placentas after giving birth, so "it seems like something humans should be doing as well."
The reason that other mammals eat the placenta after giving birth is so that predators that could eat the newborn babies aren't attracted by the smell, not because of any health benefits. Humans don't have to worry about predators trying to eat their babies.
Other things that mammals do include eating the newborns' defecation and drinking their urine and eating any offspring with physical deformities. So of course humans should be doing that too, right?
A woman interviewed in the piece aired on CTV claimed that when she takes her placenta pills, she feels like she has more energy, and produces more breast milk. It's entirely possible that any perceived benefits could be attributed to the placebo effect or a confirmation bias.
In my search to find some scientific data on this subject, all I could find was a study from the 1950s on 210 women. I couldn't find any information more recent than that.