 A Hilbert space is a vector space. This means that, for any two vectors \(|\psi\rangle\), \(|\phi\rangle\) , in the space, representing pure states, and any complex numbers \(a\), \(b\), there is another vector,  \(a |\psi\rangle + b |\phi\rangle\), that also represents a pure state. This is called a superposition of the states represented by \(|\psi\rangle\) and \(|\phi\rangle\) . Any vector in a Hilbert space can be written as a superposition of other vectors in infinitely many ways. Sometimes, in discussing the foundations of quantum mechanics, authors fall into talking as if some state are superpositions and others are not. This is simply an error. Usually what is meant is that some states yield definite values for macroscopic observables, and others cannot be written in any way that is not a superposition of macroscopically distinct states.