A Hilbert phase space is a mathematical concept that combines the ideas of a Hilbert space and a phase space. A Hilbert space is a vector space with an inner product that allows us to define distances and angles between vectors. A phase space is a space where each point represents a possible state of a physical system. A Hilbert phase space, then, is a vector space where each vector represents a possible state of a quantum system, and the inner product provides us with information about the probabilities of different outcomes.
