A compound Poisson distribution is a type of probability distribution used to describe the likelihood of something happening a certain number of times. It's like a game of chance, but instead of dealing with unbiased random chances, it takes into account all the different types of results that could happen. For example, if you flip a coin 3 times, there's a chance each time that you'll get heads or tails. The compound Poisson distribution would help you figure out the probability that you'll get a certain number of heads or tails when those 3 flips are added together.