The species is the most easily recognized unit of classification. Every organism belongs to a particular species, and while species concepts can sometimes be difficult to resolve, the idea of a group of organisms belong to a group of otherwise similar-looking organisms with which it can interbreed isnt difficult to comprehend. Above the species level, it has been traditional to recognize more inclusive groups of organisms. In the cats, we can recognize at least four genera (singular genus): Acinonyx (cheetahs), Panthera (lions, tigers, and other "big" cats), Lynx (bob-tail cats) and Felis (smaller cats). A genus is a group of species related by common descent, and the species within a genus share certain (derived) features. Proceeding up the taxonomic ladder, these genera are included in the family Felidae (all cats). The Felidae is subsequently included in the order Carnivora, consisting of other families of meat-eaters (e.g., Canidae [dogs], Ursidae [bears], and Mustelidae [weasels and otters], etc.). The order Carnivora is, in turn, placed in the class Mammalia, whose defining characteristics include hair and mammary glands. This system of classification is hierarchical, in that the taxonomic categories form groups within groups. Higher categories contain greater numbers of species, and have broader definitions. The utility of such higher levels of classification is apparent: If we know the name and classification of an organism, we automatically know a considerable amount of information about that organism and we have a system by which we can communicate new information.
The term taxon (plural taxa) refers to a taxonomic group at any level. The major taxonomic categories used in biology are:
Phylum or Division (for plants)
You should not concentrate too much on the ranks themselves - they are simply the entities into which we place smaller groups. There are "subs" and "supers" for every category, and several other categories that can be stuck in between these major groups. The binomial name of a species consists of a genus name and a species epithet. Thus, Panthera leo is the name for a lion. Eschscholzia californica is the name for the California poppy. In print, the genus and species names are always italicized or underlined. The genus name always begins with an upper case letter, and the species epithet with a lower case letter.
Every species of organism has one, and only one scientific name. This is extremely valuable to science because there will be no confusion when communicating to others about any species. In fact, there are International Codes of Nomenclature that preside over the application of scientific names. Common names are occasionally useful, but are more often sources of confusion.