Do you mean "what does it mean for ψ to oscillate in space?" This means the probability of finding the particle changes as you move through space at a given instant in time. The particle is more likely to be in some areas than others.
Do you mean "what does it mean for ψ to oscillate in time"? This means that, in a given region of space, the probability of finding the particle in that region changes over time (becoming more likely and then less likely and back again if the oscillation is sinusoidal).
This is a rather bare-bones explanation, and you need to be careful about you mean by "probability," but I think it conveys the basic answer to your question.