The "var." is indeed an abbreviation, for the word "variety" (latin "varietas").
In certain cases, it is necessary to differentiate between small changes in the genome of two members of a species; the two subjects are still the same species (they can interbreed freely) but the two subjects have marked genetic differences which are demonstrated as differences of appearance, anatomy, etc that go beyond the normal cosmetic variation commonly observed among localized or regional populations of a species.
A general synonym is "subspecies", which may be abbreviated as "sub.", "ssp." or "subsp." in the nomenclature and is used when talking about animals; in plants, "variety" is more common but "subspecies" is prevalent. More commonly, the word is removed completely and the species name consists of three words instead of two.
Another example is the tiger. All animals with the name "tiger" are of the species panthera tigris. However, there are nine "varieties" or "subspecies" of tiger: Bengal (subsp. tigris), Indochinese (subsp. corbetti), Malayan (subsp. jacksoni), Sumatran (subsp. sumatrae), Siberian (subsp. altaica), and South China (subsp. amoyensis), plus three varieties that are relatively recently extinct. If you want to talk about a "tiger" you can talk about the species panthera tigris, but most Americans talking about "tigers" are generally referring to the Bengal tiger (panthera tigris tigris) most commonly seen in U.S. zoos and traveling acts.
One more thing to be aware of is that certain species may have their species name abbreviated by convention, instead emphasizing the subspecies. The mustela nivalis or "least weasel" is the most common weasel species on the planet, and has such wide geographic variation that there are 18 documented subspecies. So, the species name nivalis is often abbreviated "n." to emphasize the subspecies (e.g. mustela n. rixosa). Things like this usually come to pass when animals formerly thought to be different species are found to be more closely related; most of the nivelis subspecies such as alleghensis, rixosa and campestri (all common in North America) were all well-known by those species names under the genus Putorious up until the mid-1900s, but the entire Mustelidae family (which also includes otters, martens, badgers, ferrets, stoats and minks) was shaken up with further research. Biologists found that the various Putorious species, and species of other Mustelidae genuses, were able to interbreed, and so were all the same species by definition, prompting a pretty deep reorganization.