Beta is conjugate prior of binomial distribution. That means is you start with prior beta, and likelihood has binomial distribution, then posterior obtained usi

Beta is conjugate prior of binomial distribution. That means is you start with prior beta, and likelihood has binomial distribution, then posterior obtained using Bayes theorem also will have beta distribution (with different paramters). If you look up definition of beta distribution and then write down formula for posterior it should be quite clear that result is also beta distribution - modulo normalizing constant which may be a little more tricky to determine.