The scientific name of a species is used as a universal name to identify that species in the scientific community. The reason such a name exists is because different languages (or even different cultures with the same language) have different terms for specific creatures, which would create a problem if two people from different regions wanted to discuss the same creature. A scientific name is also called a Latin name (as the words used are derived from Latin) or binomial nomenclature (which means, literally, something along the lines of "two-name name-calling").
The system of naming organisms, as a whole, is referred to as the Linnaean system. This system takes its name from Swedish biologist Carolus Linnaeus, who first proposed the system in 1758. Latin is used for the naming in this system because the language is dead and thus Latin words won't have any dramatically different meanings in the future. Though, technically, a scientific name could include the entire scientific classification of an organism, it typically only includes the genus and species or specific name (thus the term binomial nomenclature). The genus' first letter is capitalized and the specific name appears in all lower case letters. The human, for example, has the scientific name Homo sapiens. The genus is Homo and the species sapiens. Modern humans are classified as Homo sapiens sapiens. In this case, the additional specific name denotes that Homo sapiens sapiens is a subspecies of Homo sapiens. Another example of this can be found in the classification of the Palos Verde Blue butterfly, whose scientific name is Glaucopsyche lygdamus palosverdesensis, rather than just Glaucopsyche lygdamus.
Organisms of the same genus all have some important common trait(s) that links them. For example, plants of the genus Corynocarpus all have seeds which resemble clubs. The complete classification system for an organism begins with the name of its domain, then kingdom, phylum, class, order, family, genus, and species (and subspecies, if applicable). The full scientific name of modern humans is Eucarya Animalia Chordata Mammalia Primates Hominidae Homo sapiens sapiens. As you can probably tell, writing out or speaking the entire classification of an organism everytime it's discussed is unnecessarily cumbersome. In scientific papers, the first time an organism is mentioned, the genus and specific name are written out. Later in the document, if the organism is mentioned again and no other organisms mentioned have a different genus which begins with the same letter of the alphabet, the organism may be mentioned with the genus abbreviated to an initial. Scientific names should be italicized when possible. So, in the case of humans (in general, not necessarily modern ones), the first time they're mentioned in a paper they would be referred to as Homo sapiens but later as merely H. sapiens.