I have read that gametes of one species cannot fuse with that of another? For example the sperm of a dog can't fuse with the ova of a cat or a horse?
The implied subject of your question is the prezygotic barrier and is one of the possible determining mechanisms of speciation, the others being temporo-spatial (meaning different time or place), behavioral, and mechanical (the organisms don't fit together, physically).
Fundamentally, this means that gamete cells of each organism are chemically incompatible. While the details specific to each species vary, we can take a look at a few examples to illustrate the point.
In order for eggs of Arbacia Punctulata to attract sperm of the same species they secrete a specific chemoattractant peptide we call Resact (a selection of different species' chemoattractants can be found beyond the former link), which is adapted to diffuse well in seawater. Sperm then follow the chemical gradient in the direction of the egg, which is called positive chemotaxis. Resact doubles as an activating peptide for that species' sperm. Pycnopodia helianthoides starfish, which also reproduce through broadcast spawning, use an attractant we call startrak. Internally fertilized animals use roughly the same mechanism to guide sperm through the reproductive tract, though with different chemical adaptations specific to their evolutionary history.
Once the sperm reaches the egg, an acrosome reaction leads to the fusion of the two gametes into a potential zygote (for the reason why I say potential, see Speciation by polyploidy). The chemistry of this reaction also varies between species.
In summary, the reason is this:
- A change in gamete chemistry (chemotaxis, activation, reaction, adhesion) alters the chances of successful fertilization between one or more members of the same species.
- Thus, the altered group reproduces more often within itself than it does with the parent group, allowing it to grow in population.
- Changes in the altered group further reduce the chance of success with the parent group.
- Eventually, the chances of the altered group successfully mating with the parent group are practically zero.
This process is, of course, typically assisted by one or more of the other aforementioned mechanisms. Where two species are capable of producing offspring and successfully do so, you get hybrid speciation.