Why are plants referred to by their Latin species names, and not by their popular names?
The use of a genus-species notation gives more exact information. For example there are multiple species of chamomile: There is Roman chamomile (Chamaemelum nobile), German chamomile (Matricaria recutita, or Chamomilla recutita) and Dyer's chamomile (Anthemis tinctora). The first two species are appraised for their medicinal properties and help to calm upset tummies and to aid sleep, among other things. The latter species, however, does not have these properties and is used for dyeing. This illustrates the fact why 'chamomile' alone is insufficient.   

Popularly, classifications of living organisms arise according to need and are often superficial. Anglo-Saxon terms such as 'worm' have been used to refer to any creeping thing including snakes, earthworms and intestinal parasites. The term 'fish' is used in shellfish, crayfish, and starfish. However, there are more anatomical differences between a shellfish and a starfish than there are between a bony fish and man. 

In science it has been the convention to use the genus-species notation since Carl Linnaeus introduced it in the 1700's. This formal classification serves as a basis for a relatively uniform and internationally understood nomenclature. A uniform classification system simplifies cross-referencing and retrieval of information. The Linnaean taxonomical system aids in this purpose and is widely used. The genus-species system can be extended by including subspecies and varieties. Many (plant) species don't even have an (English) trivial name. Taking your lavender example: there are some 39 Lavendula species known and obviously, many of them don't have a trivial name. Here one has to fall back to the Latin names to be sure what it is.