Statistical independence refers to a situation where the occurrence of one event does not affect the probability of another event occurring. In other words, if two events, A and B, are independent, knowing that A has happened does not change the likelihood of B happening. This concept is crucial in probability theory and statistics, as it helps in simplifying complex problems. For example, consider flipping a coin and rolling a die. The outcome of the coin flip (heads or tails) does not influence the result of the die roll (1 through 6). Thus, these two events are statistically independent, allowing for easier calculations in probability.