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A species is a taxonomical group (specifically it is the lowest, and most precise level in the hierarchy) of organisms with similar characteristics and behaviours that are readily capable of interbreeding and producing fertile offspring. The term is somewhat loose with respect to the fact that not all people can agree when a new species has been produced by natural selection, and inbreeding is possible between different species of animals if they are closely related enough. Additionally, wildly different breeds within a species, such as with dogs, may have trouble naturally mating for practical reasons, confusing the definition of species further.
- The above definition fails for creatures which reproduce asexually, or for which the biological test "is not available".
 Problems with "species"
The term "species" is malleable. The pigeon-holing of living things into one or another specific has more to do with human classificatory systems than biological reality. Humans have attempted to categorise according to "like" and "unlike" examples of things since at least the time of Aristotle and although such systems are useful for our purposes they're not necessarily a feature of the natural world (or at least not in such simplistic terms). Most of the work in classifying into species took prior to modern genetics, and even now - with that genetic knowledge - it isn't used to thoroughly define our definitions. If anything, genetics shows that rigorous black-and-white categories like "species" aren't an especially strong idea. So any argument along the lines of speciation causes things to become different species, which means they can't reproduce, which means they'll go extinct, which means that evolution can't be true!!! (see below) is really in the formal category of not even wrong, because it tries to apply a thoroughly man-made concept to something that just happens naturally.
That isn't to say that the definition doesn't have a use. Indeed, it's the usefulness of categories and classification that lead to the term being developed. But when you use them, remember that natural behavior doesn't have to conform to the categories we develop.
 Speciation with respect to creationism
Speciation - whether a species evolve enough to diverge into a new and different species - is one of the key points that anti-evolutionists reject. In this case, they lump the ability for speciation to occur into so-called macroevolution. This is because the evidence for "microevolution" is so mind-numbingly obvious that they really cannot ignore it so must shoehorn it into a revised model; one can say that it's the only way of resolving the cognitive dissonance produced by rejecting evolution while still seeing the most blindingly obvious evidence that we can live long enough to observe. The primary problem with rejecting the idea of speciation is that it is based around the idea that the defining boundaries between species are real, solid and not flexible - something that is certainly not observed in nature or advocated by modern biology (as described above). Because of the malleability of the term, and the fact that evolution causes gradual changes, we will never see speciation (as creationists like to think of it, at least) happen. Only in hindsight, after many changes have taken place and we remove the transitions, can we see that speciation has occurred.
Slighty - and we mean slightly - more on-the-ball creationists or intelligent design advocates have come up with the concept of baraminology, which on the face of it, is similar to higher levels in the conventional biological classification, such as genus or family. A "baramin" is therefore a group of animals that contains multiple species. Baraminology was originally formulated to try and solve the problem of the high number of animals that would be on Noah's Ark, but can also be used as an excuse to accept speciation when it is conclusively observed, while still rejecting evolution. However, a baramin, unlike the biological classifications, has very little in the way of an objective description and is usually classed by fairly simple terms such as "does it look horsey or fishy" - and more often than not is extremely flexible. Hence creationists can now accept speciation, so long as you don't cross into a different baramin, which are so broad that it would be impossible to view such a change in less than a few hundred thousand years at least.