Independent events are occurrences in probability that do not influence each other. This means the outcome of one event has no effect on the outcome of another. For example, flipping a coin and rolling a die are independent events; the result of the coin flip does not change the result of the die roll. In mathematical terms, two events, A and B, are independent if the probability of both events happening together is equal to the product of their individual probabilities. This can be expressed as P(A and B) = P(A) × P(B). Understanding independent events is crucial in fields like statistics and gambling.