"Objects are simple" (2.02). As states of affairs relate to complex facts, so do Wittgenstein's objects relate to the complex objects we encounter in the world. For instance, a chair is a complex object made up of a seat, a back, and legs. The seat, back, and legs can further be analyzed into simpler parts. Objects are the basic units of this kind of analysis; they cannot be analyzed further into simpler parts.
An object has internal and external properties. The internal properties are its logical form: what kind of object it is and how it can combine with other objects in states of affairs. The external properties are what is true of it, what states of affairs it does occur in.
The internal properties of an object hold remain true no matter what. No matter what is the case, there will always be these objects with these logical forms. Thus, objects and their internal properties are what make up the substance of the world (2.021). We can imagine worlds other than this one, but we cannot imagine worlds that do not have the same logical form as this one. That is, we can imagine a world where horses speak and grass is pink, but we cannot imagine a world without space, time, or color.
Wittgenstein is careful to note, however, that the subsistence of these objects and their internal properties tells us nothing about the material properties of the world (2.0231). The material properties of the world are determined by objects being combined with other objects in certain states of affairs; that is, by the objects' external properties. For instance, the internal properties of yellow and red are indistinguishable: they are both colors and they can both occur in the same sorts of states of affairs. The only way we can distinguish red from yellow is by their external properties, by saying that certain things are true of yellow that are not true of red, and vice versa. Wittgenstein says that "substance is what subsists independently of what is the case" (2.024).
There is no metaphysical "glue" that binds objects together in particular states of affairs: "in a state of affairs objects fit into one another like the links of a chain" (2.03). The metaphor of links of a chain suggests that it is the form of the objects themselves that allows them to be combined in states of affairs. It is how objects link together that determines the structure of the state of affairs, not some properties or relations external to the objects.
Wittgenstein now comes back to where he started. Some states of affairs are the case ("positive facts") and some states of affairs are not the case ("negative facts"). Whether one state of affairs is the case or not has no bearing on whether any other state of affairs is the case or not. The world is the sum total of those states of affairs that are the case.