Later in development, however, these traits do not exist in most vertebrates and the traits that are distinctive to the different vertebrates develop. It is actually quite remarkable how similar early embryos of different vertebrate species look. One of the goals of evolutionary biology is to explain how such general patterns have evolved. An early attempt at this was made by a biologist named Haeckel. So let's see what this catchy phrase means.
Ontogeny is another name for embryonic development.
Phylogeny is, of course, evolutionary history. So, for example, in our embryonic development we go through a stage of having gill pouches like a fish, and in the distant past our ancestors were fish and had gills as an adult stage. This is an example of ontogeny recapitulating phylogeny. Haeckel was trying to put von Baer's Law in an evolutionary perspective. But there are also many examples where this does not occur.