The Poisson distribution is a statistical model used to describe the probability of a given number of events occurring within a fixed interval of time or space. It is particularly useful for events that happen independently and at a constant average rate, such as the number of phone calls received at a call center in an hour. This distribution is characterized by its parameter, λ (lambda), which represents the average number of events in the interval. The Poisson formula calculates the probability of observing exactly k events, using the equation P(k; λ) = (e^(-λ) * λ^k) / k!, where e is Euler's number, approximately equal to 2.71828.