An MCMC method for sampling one variable at a time, using the others.
Gibbs Sampling is like a potluck group chat. It keeps the menu, then changes one sad salad after checking the other dishes.
It updates one unknown at a time in Bayesian models and graph models. Exact probability is too hard there.
MCMC
Gibbs Sampling is an MCMC method using conditional samples to approach a target distribution.
PGM
In a PGM, Gibbs Sampling estimates hard posterior probabilities.
Bayesian Network
In a Bayesian Network, Gibbs Sampling samples each variable from its conditional probability.
Boltzmann Machine
Boltzmann Machine training often uses Gibbs Sampling to draw energy-based samples.