This definition is carefully constructed to identify what is genuinely independent — what requires no other thing in order to exist or to be understood. Finite things in the world depend on other things: this table depends on the wood it's made of, which depends on the trees, which depend on the soil, the sun, and so on without limit. But substance, properly understood, depends on nothing outside itself. It is its own ground and its own explanation.
Attributes are the fundamental natures through which substance is known. Extension — the property of being spread through space — is one attribute. Thought — the property of being a thinking thing — is another. Spinoza will argue that these two are not different substances (Descartes' position) but different attributes of the one infinite substance. They describe the same underlying reality from different angles.
Modes are the modifications or particular expressions of substance — the specific finite things that exist within substance. Individual human bodies are modes of extension; individual human minds are modes of thought. They do not exist independently of substance; they exist in substance and can only be conceived through it. The whole of finite reality — everything that exists in the world — consists of modes of the one infinite substance.
The most radical implication of Spinoza's definitions emerges quickly: there can only be one substance. If substance is that which exists in itself and is conceived through itself, then no two substances can share an attribute (for then they would partly depend on each other for their distinctness). Since God is defined as a being with infinite attributes, and any substance would have to have at least one attribute, there is no room for any substance other than God. Everything else — every mind and body, every thought and particle — is a mode of the one infinite substance. This is the heart of Spinoza's monism.
The definitions at the opening of Part I of the Ethics are deliberately few and stark. Spinoza's geometric method — definitions, axioms, propositions, proofs — creates the appearance of mathematical certainty, though philosophers have contested each step from the definitions onwards.
