Short answers, pulled from the story.
A species is the basic unit of classification and a taxonomic rank below genus. It is most often defined as the largest group of organisms in which two individuals of the appropriate sexes can produce fertile offspring, a definition Ernst Mayr formalised in 1942 as the biological species concept.
The biologist R. L. Mayden recorded about 24 species concepts, and the philosopher of science John Wilkins counted 26. Wilkins grouped them into seven basic kinds, including agamospecies, biospecies, ecospecies, evolutionary species, genetic species, morphospecies and taxonomic species.
Every species except viruses receives a two-part name called a binomen, made of the genus name followed by the specific name or epithet. In Boa constrictor, Boa is the genus and constrictor is the specific name, and the name becomes official when a type specimen is formally described in an accepted publication.
The most recent rigorous estimate puts the total number of eukaryote species between 8 and 8.7 million. About 14 percent of these had been described by 2011.
Defining a species is hard because evolutionary processes cause species to change, and several cases break simple definitions. These include asexual organisms, fossils that cannot be bred, hybridisation that permits gene flow, ring species, microspecies aggregates, and horizontal gene transfer. This difficulty is known as the species problem.
DNA barcoding uses a single easy-to-apply locus to distinguish species, such as the 16S ribosomal RNA gene in bacteria or a region of the cytochrome c oxidase gene in eukaryotes. The Barcode of Life Data System holds DNA barcode sequences from over 190,000 species.
A viral quasispecies is a group of genotypes related by similar mutations, competing in a highly mutagenic environment and governed by a mutation-selection balance. It is used because viruses mutate too rapidly for conventional species concepts to apply, and it does not resemble a traditional biological species.