Ernst Haeckel (1834–1919), a German biologist and naturalist, disagreed with von Baer and further expanded on the Meckel–Serres law with his biogenetic law. What does the biogenic law claim?

Simply it states that the  progress of development of an organism is a recapitulation of the organism's evolutionary history, and thus its progeny.

Explanation:

Hence based on this  the stages of developments of  an  embryo  are similar to developments stages seen in  adult forms.Therefore it  is can be stated as recapitulation of  phylogeny by ontogeny . Thus the developmental stages observed in  an embryo, are summary oft he adult forms of  its  progeny.Therefore, studying this  developmental stages in an embryo is in effects studying the diversification of life on earth, and its history.

In summary the developmental stages of the embryo is a good method  to detect the similarities between  taxa, and findings from these can provide evidences that  their is a common ancestry  for  all species of organism on earth.