The Born rule gives the probability distribution of particle positions from a wavefunction.
For a position-space wavefunction ψ, the probability density is the squared magnitude |ψ|². Integrating this density over a region gives the probability of finding the particle there. The wavefunction itself can have complex values and is not directly interpreted as an ordinary measurable wave; its squared magnitude supplies the observable position probabilities.
Max Born proposed this statistical interpretation in 1926. It changed the role of quantum mechanics from a theory predicting definite microscopic trajectories to one predicting distributions of measurement outcomes. The rule also applies more generally: the squared amplitude associated with an outcome determines its probability.
A normalized wavefunction has total probability one across all possible positions. Interference occurs because amplitudes are added before their squared magnitude is calculated. That is why alternatives can reinforce or cancel one another, producing patterns that cannot be explained by simply adding classical probabilities.