Electrons do not spin around the nucleus in perfect circles like planets. They act like fuzzy clouds of energy that behave like both particles and waves. The wave function is the math equation that captures this strange dual behavior.
Chemists use the Greek letter psi (Ψ) to stand for this mathematical function. The wave function itself does not have a physical form that you can touch. However, if you square the absolute value of the function, you get something very useful.
The squared value tells you the exact probability of finding an electron in a specific spot. This map of probabilities creates the distinct physical shapes we call electron orbitals. The familiar spherical shapes and dumbbell shapes in textbooks are visual pictures of these squared functions.
A common student misconception is that the wave function shows the exact path an electron travels. In the strange world of quantum mechanics, we can never know the exact traveling path. We can only know the mathematical chances of finding the electron in a given area.
Every valid wave function must add up to a total probability of exactly one. This rule simply means the electron must definitely exist somewhere in the entire universe.