Every physically-realizable state of the system is described in quantum mechanics by a state function $$\psi$$ that contains all accessible physical information about the system in that state.
The properties of a quantum mechanical system are determined by a wavefunction Ψ(r,t) that depends upon the spatial coordinates of the system and time, $$r$$ and $$t$$. For a single particle system, r is the set of coordinates of that particle $$r = (x_1, y_1, z_1)$$. For more than one particle, $$r$$ is used to represent the complete set of coordinates $$r = (x_1, y_1, z_1, x_2, y_2, z_2,\dots x_n, y_n, z_n)$$. Since the state of a system is defined by its properties, $$\Psi$$ specifies or identifies the state and sometimes is called the state function rather than the wavefunction.