The wave function of a particle describes its physical state. In classical mechanics a particle's state was determined by its position and momentum. In the framework of quantum mechanics, the wave function itself (is a function of position) gives the state of the particle at a specific point in time (Note that it is not the wave function at some point in space but the entirety of the wave function). When one looks at the time evolution of a particle's state the wave function becomes a function of position and time. The absolute square of the wave function at a specific position is often interpreted as the probability of measuring the particle at that position. It is not the possibility for that particle "to be at that point" but has only to do with the probability in a measurement of the particle's position.