It's a way to approximately draw samples from a probability distribution. Crucially, it applies even when we only know the distribution up to a multiplicative constant which is a common ailment of many distributions in the computational uncertainty quantification field (not that we don't know the constant, but that it's usually computationally catastrophic to estimate it well).
MCMC = Markov Chain Monte Carlo
It's a way to approximately draw samples from a probability distribution. Crucially, it applies even when we only know the distribution up to a multiplicative constant which is a common ailment of many distributions in the computational uncertainty quantification field (not that we don't know the constant, but that it's usually computationally catastrophic to estimate it well).