Strictly speaking, the existence of vegetative life is impossible to demonstrate because it depends on the interpretation that one gives to the basic fact that there are living things whose matter is organized in precise and characteristic ways. If biology can be reduced to physico-chemical forces acting in cells, then cells are identical to chemical compounds, and life can be considered by no one other than physicists and chemists. The question is whether living things require some principle over and above the material constituents in order to explain their existence and behavior. The belief that there is required no further principle is a belief almost all physicists and chemists bring to the study of living things.
There are indeed physical and chemical processes and forces active in cells and plants. But these forces are instruments working for the sake of the good of the whole in such a way that the whole is self-perfective. There are at least three ways in which the physico-chemical forces are subordinated to the good of the whole. These are known as nutrition, growth and reproduction. Nutrition is directed to the conversion of non-living matter into living matter. Growth is directed to the perfection of quantity, i.e. the fully developed structure of the particular organism, in accordance with the individual nature of that particular organism. Reproduction is directed to the generation of new individual living substances, that is, to the conservation of the species.
The vegetative part has three powers. For the vegetative part has for its object the body itself, living by the soul; for which body a triple operation of the soul is required. One is that whereby the body acquires existence. The generative power is directed to this. Another is that whereby the living body acquires due quantity. The augmentative power is directed to this. Another is that whereby the body of a living thing is preserved in its existence and in its due quantity. The nutritive power is directed to this.(Summa Theologiae Ia 78, 2.)
The nutritive soul is found along with all the others and is the most primitive and widely distributed power of the soul, being indeed that one in virtue of which all are said to have life.Aristotle, De anima II, 4 (415a23-25)
Nutritive activity is a mode of being of the cells, as fundemental as structure and form. As soon as their chemical exchanges and metabolism cease, the organs come into equilibrium with their medium and die. Nutrition is synonymous with existence.A. Carrell, Man the Unknown, p.24
For St. Thomas, the most important function of vegetative life is reproduction:
The nutritive and the augmentative powers have their effect where they exist, since the body itself, united to the soul, grows and is preserved by the augmentative and nutritive powers which exist in one and the same soul. But the generative power has its effect, not in one and the same body but in another; for a thing cannot generate itself. Therefore the generative power, in a way, approaches to the dignity of the sensitive soul, which has an operation extending to extrinsic things, although in a more excellent and more universal manner. Therefore, of these three powers, the generative has the greater finality, nobility, and perfection…for it belongs to a thing which is already perfect to produce another like unto itself, and the generative power is served by the augmentative and nutritive powers; and the augmentative power, by the nutritive.(Summa Theologiae Ia 78, 2.)
The vegetative soul.
The soul of the plant is called “material”, not because it is composed of matter, but because it is intrinsically dependent upon matter for its becoming and its being. This is a conclusion we derive because all the operations of a plant (nutrition, growth, generation, etc.) are intrinsically dependent upon matter. The operation follows the being, hence the vegetative soul is called material. The vegetative soul comes from the potency of matter and goes back to the potency of matter when the plant is corrupted. Since its operation is dependent on matter, its being is likewise dependent on matter.