When doctors say that fetuses prove evolution, what are they referring to?

Old argument: It's moot. Comparing the sequenced genomes of living creatures leaves no doubt whatsoever about common ancestry rather than just "common design." Even Billy Graham now believes in evolution. The fact that early forms of living things look identical for quite a while should perhaps simply make you more appreciative of what we have in common with other animals. Best wishes.

Not doctors: Evolutionary biologists say, or rather said, that "ontogeny recapitulates phylogeny." It refers to the observation that vertebrate embryos resemble earlier forms during development; eg humans briefly have tails early on. It's true that all vertebrate embryos look alike early on, but the similarity quickly disappears & piscine, amphibian, reptilian, mammalian & avian lines of development supervene.