A single microcosmic particle is suitably described by a quantum mechanical equation like Schroedinger equation or Dirac equation. The equation is a differential equation for the time development of the state function, in general termed psi-function. The time development is deterministic, but the state function is considered a probability.
The collapse of the wave function is the brutal name for the fact, that observations on the mesocosmic level terminate the unitarian development of the state function and project the state function into one distinguished state, often belonging to a discrete set of possible states. This model (Copenhagen interpretation) solves the problem how to apply quantum mechanics, but it does not explain why nature acts according to these two incompatible descriptions.
In the last decade the effect of decoherence seems to establish a smooth transition from the microcosmic to the mesocosmic description. Continous interactions of the particle with its environment reduce and finally erase the possibility of the state function to interfere with itself and to realize different possibilites. Apparently, this kind of interaction is not bound to the interaction with a human observer. Hence decoherence also holds for particles traveling through the interstellar space, which is not empty.
For a gentle introduction to decoherence see the chapter "Decoherence and Quantum Reality", p. 208ff in Greene, Brian: The Fabric of Cosmos (2004).
For a textbook with contributions from several experts see Giulini, D. et al.: Decoherence and the Appearance of a Classical World in Quantum Theory (1996).