In biology, this is known as Biogenetic Law, which Thain & Hickman (1994: 67) describe as:
Notorious view propounded by Ernst Hæckel in about 1860 (a more explicit formulation of his mentor Muller's view) that during an animal's development it passes through ancestral adult stages ('ontogenesis is a brief and rapid recapitulation of phylogenesis'). Much of the evidence for this derived from the work of embryologist Karl von Bær. It is now accepted that embryos often pass through stages resembling related embryonic, rather than adult, forms.
Applied to language, the notion that ontogenesis recapitulates phylogenesis would mean that during the development of language in the child, it passes through ancestral adult stages, such that, for example, the ontogenesis of English involves passing through Proto-IndoEuropean, Proto-Germanic, Anglo-Saxon and Middle English stages.