Species, speciation... and definitions

 A species is a population on individuals that can interbreed and produce viable offspring. In order for offspring to be viable they need to be able to reproduce. Everyone knows the example of a horse and a donkey, they can mate and produce offspring (the mule) but the mule is sterile, therefore we know that a horse and a donkey are two different species.

Another example is the shark and the dolphin, many people think they are the same species or at least closely related because they have similar traits but they aren't. However a chihuahua and a Great Dane look very different in many aspects including huge differences in size and they are the same species and could very possibly (yet difficultly) mate and produce viable offspring.