Many gardeners ask "Why can't we just use common names?". The main hurdle is that plants are introduced from all over the world and therefore do not have common names in the language of the recipient country. It is of course possible to invent common names in the language of the country. In fact, this is already done extensively in the United States, but with no system to regulate or standardise names, confusion can easily arise.
A classic example in the English speaking world is Bluebell, referring to Hyacinthoides non-scripta in England, Campanula rotundifolia in Scotland, Sollya heterophylla in Australia and species of Mertensia in North America. The scope for confusion is enormous.
Most people do not think twice about using Rhododendron, Chrysanthemum or Fuchsia, common names for three large groups of plants. The fact that they have passed into common usage demonstrates the great strength of botanical names - they are intended to be universal. The aim of the botanical naming system is to provide each different plant with a single name which can be recognised by anyone, whatever their own language.
What do the parts of a scientific name mean
Take as an example Digitalis purpurea. The first word is that of the 'genus', which includes all foxgloves. (Plants which share a number of significant features are grouped together to form a 'genus', in plural 'genera') The second word is the 'species' (species can be defined as a group of interbreeding individuals producing more-or-less similar offspring and differing from other similar groups by a number of key characters). These two words together (Digitalis (1) and purpurea (2) refer uniquely to the purple-flowering foxglove in W. Europe.
Digitalis grandiflora is a yellow-flowering species from C. and S. Europe. Sometimes a species is subdivided into subspecies (subsp.), varieties (var.) or formas (f); for example the white flowering variants of the purple foxglove is called; D. purpurea f. albiflora.
What is a cultivar?
In cultivation, variation within species and that generated by hybridisation is particularly valued. Plants exhibiting desirable characteristics of flower colour, habit, size, variegation, fruit colour, flavour etc. are often given names. These are termed cultivars (from cultivated variety). For example, a foxglove with variegated leaves has been given the name Digitalis purpurea 'Chedglow'. If there can be no confusion, the genus and the cultivar names may be used without the species name. Solanum tuberosum 'King Edward', Solanum 'King Edward' and even potato 'King Edward' are equally correct. However, 'King Edward' alone could be confused with the unrelated Achillea x lewisii 'King Edward.
What is a hybrid?
A cross made between plants of two different species results in a plant called a hybrid. This hybrid may be given its own scientific name. Thus Digitalis x mertonensis is the hybrid name for all plants derived from the cross between D. purpurea and D. grandiflora. The 'x' indicates the hybrid status. Many different cultivars may result from the same cross.
Bibliography: The Royal Horticultural Society Botany Advisory Services, January 2006