Merriam-Webster Dictionary defines a plant as:
(noun) 1 a : a young tree, vine, shrub, or herb planted or suitable for planting.
b : any of a kingdom (Plantae) of living things typically lacking locomotive movement or obvious nervous or sensory organs and possessing cellulose cell walls.
2 a : the land, building, machinery, apparatus, and fixtures employed in carrying on a trade or an industrial business.
b : a factory or workshop for the manufacture of a particular product.
c : the total faciluties available for production or service.
d : the building and other physical equipment of an institution.
Why were Plants created and for what? This all starts very far into the future in a flashback, for the benefit of the Trigun timeline. Basicly we humans pollute the earth beyond repair. So not wanting to die with the planet we send our SEED (A small country worth of humans) into space to start all over on a new world. To prevent the human from being completely helpless when they get to the new world they created Plants. Plants are a new technology. They are living machines which produce little to no waste. (Later refered to as operating outside the realm of normal mathematics and logic.) On top of that they are capable of a wide range of function. Some plants produce electricity, other water. These Plants could also make clothes and other machines. The greatest thing about these plants were they produced more than they consumed. The were easy to operate, and needed little supervision.
Now how did Vash and Knives come into existence? Obviously traveling to another planet takes a while. Which means someone has to check to make sure the Plants a operating okay. This is where the SEED crew comes in. These five people were chosen to oversee the rest of project SEED. They have to make sure the cryogenic pods are operating, look for a suitable planet, and maintain the Plants. One day while checking on the Plants the crew finds two 'babies.' Unexpectedly they were created by a plant. Unlike their brotheren these plants are not restricted to the 'Bulb World.' They have free will. Now being born from a Plant they were endowed with all of their abilities. A near infinite lifespan, communication with other plants, the ability to generate surplus energy, and other special traits.
Now just what is a Plant? This is my hypothetical logic to it. Plants are the new generation of human slaves. You remember back in the late 70's early 80's the whole test tube baby experiment? If you don't then I'll bring you up to speed. A test tube baby was an embryo that was grown to maturity in a lab. A baby that is grown and born outside the womb. Now a Plant is breed the same way, but with genetic modifications. Unlike the test tube baby a Plant is born into a Bulb. The Bulb is a machine that enhances, harnesses, and focuses the geneticly modified gift of the Plant. Now why did I call them slaves? For one a Plant has no rights or free will. There whole existence is to work. They aren't given the chance as others are to do normal thing because they never allowed to leave the Bulb. They never rest, and the only outside associations they have are by telepathy with other Plants.