Botanical Names
The Latin plant names used in medieval and renaissance herbals do not correspond to the modern scientific names.  The modern nomenclature was not developed until the 18th century.
The modern scientific name is made up of a genus name and a species name.  The genus is a category that contains one or many species.  The individual species may also have a variety and/or cultivar name.
genus a group of related (having similar physical characteristics) plant species
the genus name is always capitalized
species members of the genus that are distinct from each other are labeled as individual species
the species name is always in lower case letters
variety a naturally-occuring variation within a species
the variety name is sometimes preceded by "v." or "var."
cultivar a variation (within a species) that is man-made and does not exist outside of cultivation
cultivar names are shown in single quotes
hybrid a man-made hybrid (or cross) between two species
sometimes indicated by an "x"
common name folk name
common names vary from place to place and are reused over time for different plants
To illustrate how the system works, here are the scientific and common names for a few plants (don't look for these at your local nursery):
Genus
Species
Variety
Cultivar
Common Name
Aconitum napellus v. alba 'Lucretia Borgia' White Monkshood 'Lucretia Borgia'
Helleborus foetidus flore pleno   Double Stinking Hellebore
Papaver somniferum   '1040 EZzzz' Opium Poppy '1040 EZzzz'