2. Accessibility. If you use the scientific name, everyone will know exactly what plant you are talking about. Not only that, you will instantly gain access to huge amounts of knowledge about plants!
Theophrastus developed the first known formal system of plant classification about 300 BCE, but the modern system wasn't developed until the 18th century. Carolus Linnaeus created a consistent hierarchical system for naming all organisms. Before that, plants were named using a multiword description, and that description wasn't necessarily consistent between authorities.
The Linnaean system uses "binomial nomenclature", meaning that the essential form of a plant name has two parts: genus and species. The Genus is capitalized, the species is not, and both are italicized.
Here's the whole system, for plants:
KINGDOM Plantae DIVISION (= PHYLUM for animals) CLASS ORDER FAMILY (ends in -aceae, important for plant taxonomy) Genus species
You often see a third part, something like: Plantago major L. The third part of the name is the authority, the botanist who named that species. Species with an L. were named by Linnaeus himself. The goal of modern taxonomists is to develop a classification scheme that shows true evolutionary relationships. As botanists learn new information about these relationships, they do change plant names to reflect that. The name of person doing the changing is added to the end to help keep things straight. (There is an international authority in charge of all this.)
Sometimes, especially in garden catalogs, species names may also have variety (var. suchandsuch) or cultivar names "GrowMe" attached. (The difference is that varieties occur naturally, but aren't distinct enough to be separate species, while cultivars must be raised in "captivity" to remain distinct.)
As medievalists, we have a special interest in the scientific names. The names of common European plants are usually derived from the longer descriptive names already in use, and almost always tell us something interesting about the plant (once you learn a bit of Latin vocabulary).
officinalis: medicinal vulgaris: common oleraceus: kitchen vegetable rugosum: wrinkled sativus: cultivated arvensis: of the fields
Most people already know some of the really hard scientific names, like Asparagus and Chrysanthemum. Medievalists will recognize even more - Petroselinum, for example.
And it's even easier than Latin - botanical Latin isn't even remotely grammatical (usually the genus and the species have the same ending), and isn't pronounced in a way that would make Latin scholars happy. Just say whatever makes sense to you - somewhere there is a botanist who agrees.
The PLANTS database includes many useful features: