Can you please explain 'Ontogeny recapitulates Phylogeny'?

Ontogeny recapitulates phylogeny is credited to Ernst Haeckel. The theory has been discredited since its development. Ontogeny is a word used to refer to the changes in size and shape that occur during the embryological development of an organism. Phylogeny refers to evolutionary history (think of an evolutionary tree that shows the branching pattern of species evolution over time).  According to Haeckel, the developmental changes that occur in an embryo before birth mimic the adult forms of the ancestors of an "advanced" organism, with early stages resembling the adult forms of the most distant ancestors. His theory also contends that, over time, developmental stages are added leading to speciation and branching of the phylogenetic tree. So, if you were to track an embryo of an organism at the top of a phylogenetic tree, the stages of development would resemble (or at least share some characteristics with) the adult forms of all of the species in the path of that species' evolution, starting with the species at the bottom of the tree and working up toward the focal species. One example would be the pharyngeal slits or folds that are visible during human development. Haeckel claimed that they were reminiscent of the gills of fish which share a distant relative with humans. Haeckel supported his idea with drawings, but has been found to have overemphasized structures supporting his theory.

The updated version of the theory contends only that during development, species go through similar developmental processes constrained by shared gene complexes (for example, Hox genes). If you view developing embryos of mammals, for example, you will see that the stages of development progress in the same order. This is controlled by genetics and demonstrates that all mammals have a common ancestor that also had the same sets of developmental genes.