Two events, A and B, are statistically independent if the probability of their joint occurrence is equal to the product of their individual probabilities. This can be mathematically expressed as P(A and B) = P(A) * P(B). If two events are independent, knowledge of one event gives no information about the other. This concept is crucial in many fields, including statistics, machine learning, and data analysis, where the goal is often to understand relationships among variables without attributing influence improperly.