An independent event in probability refers to an occurrence where the outcome of one event does not affect the outcome of another. For example, flipping a coin and rolling a die are independent events because the result of the coin flip has no impact on the result of the die roll. In mathematical terms, two events A and B are independent if the probability of both occurring 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.