Unfortunately, in practice, this definition is plagued by ambiguities. To begin, this definition is not relevant to organisms (such as many types of bacteria) that are capable of asexual reproduction. If the definition of a species requires that two individuals are capable of interbreeding, then an organism that does not interbreed is outside of that definition.
Another difficulty that arises when defining the term species is that some species are capable of forming hybrids. For example, many of the large cat species are capable of hybridizing. A cross between a female lions and a male tiger produces a liger. A cross between a male jaguar and a female lion produces a jaglion. There are a number of other crosses possible among the panther species, but they are not considered to be all members of a single species as such crosses are very rare or do not occur at all in nature.
Species form through a process called speciation. Speciation takes place when the lineage of a single splits into two or more separate species. New species can form in this manner as a result of several potential causes such as geographic isoloation or a reduction in gene flow among members of the population.
When considered in the context of classification, the term species refers to the most refined level within the hierarchy of major taxonomic ranks (though it should be noted that in some cases species are further divided into subspecies, but that term lacks clear and consistent definition).