Markov Chain Monte Carlo is a method used to estimate statistics in complex models by simulating random selections. It creates a chain of random selections where the final distribution matches the desired one. This technique is helpful for analyzing complex Bayesian models, especially for posterior distributions. The Metropolis-Hastings algorithm involves selecting items from a proposal distribution and deciding whether to keep them based on a rule. The Gibbs sampler is a specific case where the proposals are conditional distributions of individual parts of a parameter vector. This method has various applications and can be used in different scenarios.