The Beta distribution is the probability distribution of a probability.
For example, let p be the probability of some event happaning. Assume that we don't know p exactly, but know that p should lie within approximately [0.1, 0.35], and is most likely about 0.2. Then we may use the Beta(20, 80) distribution to represent this knowledge, because its mean value is 20/(20+80) = 0.2 and it lies almost entirely within [0.1, 0.35].
More along these lines: https://stats.stackexchange.com/a/47782
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