MCMC methods help us in estimating the posterior distributions via sampling from a complicated probability distribution. It is a non-parametric approach to estimating the posterior distribution and as such, with enough iterations it can converge to the expected distribution. As the name suggests, it consists of 2 parts: Monte Carlo and Markov Chain.

Monte Carlo: a technique to randomly sample a distribution to help approximate the desired quantity. Example: calculating the value of $\pi$ .

Markov Chain: a way to generate a sequence of random variables where the current number depends on the previous value. Markov Chain is essentially a random walk on a state-transition graph. Thus, the idea here is that this chain of drawn numbers will settle when repeated for a large number of times.