Botanical nomenclature is the formal, scientific naming of plants. It is related to, but distinct from taxonomy. Plant taxonomy is concerned with grouping and classifying plants; botanical nomenclature then provides names for the results of this process. The starting point for modern botanical nomenclature is Linnaeus' "Species Plantarum" of 1753. Botanical nomenclature is governed by the "International Code of Nomenclature for algae, fungi, and plants" ("ICN"), which replaces the "International Code of Botanical Nomenclature" ("ICBN"). Fossil plants are also covered by the code of nomenclature. 

Within the limits set by that code there is another set of rules, the "International Code of Nomenclature for Cultivated Plants (ICNCP)" which applies to plant cultivars that have been deliberately altered or selected by humans (see cultigen). 

Botanical nomenclature has a long history, going back beyond the period when Latin was the scientific language throughout Europe, to Theophrastus (c. 370–287 BC), Dioscorides (c. 40 – 90 AD) and other Greek writers. Many of these works have come down to us in Latin translations. The principal Latin writer on botany was Pliny the Elder (23–79 AD). From Mediaeval times, Latin became the universal scientific language (lingua franca) in Europe. Most written plant knowledge was the property of monks, particularly Benedictine, and the purpose of those early herbals was primarily medicinal rather than plant science "per se". It would require the invention of the printing press (1450) to make such information more widely available.
Who started it?
Linnaeus