In essence, this is thought as, “What happens next depends on the state of things right now.” While the present is known, the past and future are independent, ie Memory-less. The MCMC uses the markov chain as the basis for simulating sampling from complex probability distributions.
graph TD A((State A)) --> |0.7| A A --> |0.3| B((State B)) B --> |0.4| A B --> |0.6| B
It significantly reduces the number of parameters when studying any complex process. The most ubiquitous examples are Google’s Page rank and next word prediction.