All known extant species use the same chemical structures to perform the functions considered definitive of life. Scientists have identified countless alternative structures that could perform the same functions, and apparently could perform them just as well, but they are not used by any known organism. Inheritance of the common structure from a common ancestor would explain this.
A precise definition of life remains subject to debate, but there is a widespread consensus that a thing is alive if and only if it exhibits the following four characteristics.
In Darwin's day, nothing was known about heredity except that it happened. The mechanism was a complete mystery. After the Origin of Species was published, it took the scientific community almost 100 years to discover DNA and then figure out how it works. There is no known natural reason why each species could not have had its own genetic code. Had it been discovered that different species did in fact have different codes, the theory of common descent would have become virtually indefensible. The theory could yet be dealt a serious challenge by the discovery of some species that does use a different genetic code. The fact that all species that are so far known use the same code is easily explained by supposing that all species are related by descent from a common ancestor.
The same holds for all other chemicals vital to life functions. In each case, of the hundreds of variations possible, few are used. This is easily explained by supposing they were inherited from a common ancestor.
There are variations, but even those variations, as observed, are consistent with that supposition. The variations are greatest between species for which one would expect the common ancestor to be most distant. Species that look more closely related exhibit less chemical variation.
Like the genetic code, this too is confirmed every time a new species of any kind is found. If a fish is ever discovered, for example, with hemoglobin identical to human hemoglobin, the theory of descent with modification is going to be in trouble. It will also be in trouble if any species is ever discovered using an oxygen-transport chemical that is quite unlike the hemoglobin of any other species.
Next: The facts: Transitional forms