Old English plante "young tree or shrub, herb newly planted, a shoot or strip recently sprouted from seed," from Latin planta "sprout, shoot, cutting" (source of Spanish planta, French plante), which is perhaps from an unattested verb *plantare "to drive in with the feet, push into the ground with the feet," or perhaps "to level the earth," from planta "sole of the foot," from nasalized form of PIE root *plat- "to spread." German Pflanz, Irish cland, Welsh plant also are from Latin.
Broader sense of "any small vegetable life, vegetation generally" (sometimes popularly excluding trees), "an individual living being with material organization but not animal in nature" is recorded by 1550s.
Most extended usages are from the verb, on the notion of "something planted;" such as "construction for an industrial process," 1789, at first with reference to the machinery, tools, apparatus, etc., later also the building; also slang meaning "a spy" (1812). Many of these follow similar developments in the French form of the word.