Spinoza proves this proposition from his earlier metaphysics. Every finite thing is a mode of the one infinite substance, expressing the power of that substance in a particular determinate way. Nothing in a thing's own nature could destroy it — for its nature is precisely what it is, and to destroy that nature would be self-contradictory. Therefore every thing, by its own internal nature, tends to persist. Destruction can only come from outside — from the interaction with other modes more powerful than itself.
This is the most radical form of the doctrine: conatus is not a property that things happen to have — it is what they are. The essence of each thing just is its power of self-persistence, its drive to continue being what it is. In human beings, this drive takes two forms depending on which attribute we describe it through: as body, conatus is appetite; as mind, it is will. Desire — conscious appetite — is conatus at the level of awareness. What we want, at the deepest level, is simply to continue existing.
The concept of conatus provides the foundation for Spinoza's ethics. Good, for Spinoza, is not a feature of objects that exists independently of the striving beings who pursue them. Good is whatever genuinely helps a being to persist and flourish; bad is whatever diminishes or impedes that striving. This makes ethics naturalistic: to understand what is good for human beings, we must understand what kind of beings we are and what genuinely promotes our persistence and power of action. The highest good — rational understanding — is the highest because it most completely expresses and extends human conatus.
Conatus is introduced in Propositions VI and VII of Part III of the Ethics. The concept draws on a long tradition — Hobbes had used similar language about the natural striving of bodies — but Spinoza integrates it into a complete metaphysical system in a way that was unprecedented.
