The wave function, also called Schrodinger's Equation, is a mathematical description of all the possibilities for an object. For example, we could imagine the wave function as a deck of 52 cards where each card is a yet unobserved quantum state. The deck has 52 possibilities so the wave function has 52 humps.
In quantum theory, all events are possible (because the initial state of the system is indeterminate), but some are more likely than others. While the quantum physicist can say very little about the likelihood of any single event's happening, quantum physics works as a science that can make predictions because patterns of probability emerge in large numbers of events. It is more likely that some events will happen than others, and over an average of many events, a given pattern of outcome is predictable. Thus, to make their science work for them, quantum physicists assign a probability to each of the possibilities represented in the wave function.
Excerpt from the Encyclopedia Britannica without permission.