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The modern theory of evolution differs enormously from Lamarckian evolution. For example, traits are now known to be inherited separately from each other, rather than as a whole representing phylogenetic changes. Adaptations are known to result from natural selection acting on variations within a population, not from use or disuse of an organ. Modern evolutionary theory has no room for Haeckel's version of recapitulation. Yet his original observation, that embryos resemble each other at early stages of development, remains.
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For example, the notochord is a structure that was present in the first fishes to swim the oceans. It is a thin flexible rod located in these fishes' backs that helped stiffen the body and conserve momentum in the animal's side-to-side swimming motion. Only a few modern species, such as lampreys, have notochords as adults, yet this structure is present in all vertebrate embryos. (In fact, the term "chordate" refers to the notochord, not the spinal cord as may seem to be the case.) Located ventral to the neural tube, it plays an important role in the organization of a developing vertebrate, and elements derived from it appear in the vertebral column.
A principle of biological development is that it proceeds more like a recipe than like a blueprint. Each stage relies on the stage before it. Every species of vertebrate is a variation on the basic vertebrate body plan; thus each vertebrate embryo starts out appearing very much like this basic plan, and the modifications derived through evolution are then applied to it. More closely related species have more of these modifications in common, and these modifications typically appear later in development.
For example, at a particular stage of development, a cat embryo and a human embryo resemble each other more than either resembles a fish embryo, reflecting the fact that cats and humans (both mammals) are more closely related to each other than to fishes. Likewise, at another particular developmental stage, a cat embryo and a dog embryo resemble each other more than either resembles a human embryo, reflecting the fact that cats and dogs (both carnivorans) are more closely related to each other than to humans.
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Comparative embryology provides data, therefore, which can be used with the now-standard discipline of cladistics to help uncover phylogeny. It is one tool in the phylogenist's toolbox, along with other tools like fossils, anatomy, genetics, and biogeography.
In current scientific parlance, then, "ontogeny recapitulates phylogeny" means that many developments take place during ontogeny in roughly the same order that they took place in during phylogeny. This is a result of the way evolution acts on what it has available to it, rather than a causative mechanism in itself. Though Haeckel's ideas have been rejected in their most literal form, his observations have helped understand the history of evolution.