In the late 19th century, a German zoologist named Ernst Haeckel proposed a theory according to which embryonic development is essential a condensation of historical evolutionary development. Haeckel coined a very catchy phrase to describe this process: "Ontogeny recapitulates phylogeny," and the lay public became somewhat enamored of it.
According to Haeckel's theory, a human or any other mammalian embryo starts out basically as a fish, then becomes an amphibian, then a reptile, and finally a mammal. Although the general public loved the idea and some scientists were initially attracted to it, by the early 20th century biologists had discarded it in the face of abundant contrary evidence.
Most unfortunately, Haeckel was not only wrong but dishonest. It was discovered not long after he published his work that he had doctored some of his drawings of embryos to make them more nearly consistent with his theory. In the end, though, his theory was discredited by the evidence, not the ethics of its proponent.
Slogans can take on a life of their own, however, and it is still widely believed that "ontogeny recapitulates phylogeny" is some kind of evolutionary law. It is not, and it has been over a century since any significant number of biologists thought it was.
Nevertheless, embryonic development does present evidence for common ancestry and descent with modification. The evidence just isn't exactly what Haeckel thought it was.
There is a stage at which the embryos of fish, amphibians, reptiles, and mammals look very much alike -- although not indistinguishable, as Haeckel might have led people to believe -- and what is relevant to our discussion is that the common features include structures (such as gill pouches) that are characteristic of fish but not any of the other groups. The fish embryo then takes its own developmental path and proceeds to look more and more particularly like a fish. Meanwhile, the other embryos continue looking a lot like each other.
Their common characteristics now include things that are distinctly amphibian -- including, still, those gill structures that some amphibians need during their larval stages. But then the amphibians go off on a developmental tangent while the reptile and mammal embryos keep up the near-twin act. At this embryonic stage, for example, it would be very hard to distinguish the various head bones -- skulls and jaws -- of reptiles and mammals. The size, shape, number, and placement of the various parts are pretty much alike.
If you could watch from this point on, you would notice among other things that a certain set of bones became part of the jaw in the reptile while those very same bones ended up in the ear of the mammal.
And, of course, both reptiles and mammals lose those gill pouches before they're born.
Here is another example. As the circulatory system begins to develop, all the embryos originally develop a two-chambered heart with two aortic arches. Adult fish have two-chambered hearts with two aortic arches, and so there is no change in this structure as the fish embryo develops. The mammal embryo, though, eventually loses one aortic arch, and meanwhile each of its two heart chambers subdivides to result in a four-chambered heart.
There are a couple of other points that similarly suggest common descent with modification. Fish embryos never develop legs. The others do -- all of them. Snake embryos lose those legs before they are born. The embryos all have tails through most of their development, too, but a few mammals lose them before birth. Also, none of the embryos ever grows hair or nipples unless it is a mammal embryo. Some mammals (such as whales) that are normally born hairless do grow hair while embryos but lose it before birth. This occasionally happens with human embryos as well. But it never happens to non-mammalian embryos.
Fossils of animals that look ancestral to elephants all have four tusks, two in the upper jaw and two in the lower. Modern elephants have tusks only in the upper jaw, but their embryos always grow four tusks, losing the pair in the lower jaw before birth.
Porpoise embryos develop rudimentary hindlimbs that are lost before birth. Their forelimbs develop initially with five separate digits that later becomes fused into flippers. Its nose appears first on the tip of its snout, migrating to the top of the head before birth.
Embryonic birds start with five digits on each limb, just like all other vertebrates.
Descent with modification accounts for all of this. These facts are what we would expect to observe if fish existed before any amphibians existed, and amphibians existed before any reptiles existed, and reptiles existed before any mammals existed, and if amphibians were modified fish, reptiles were modified amphibians, and mammals were modified reptiles.
This is not to suggest that these facts of embryology can have no other explanation. But they do have that possible explanation, and that makes them evidence for evolution.