The Gibbs sampler is a form of Markov Chain Monte Carlo simulation.
It is based on sampling from full conditional distributions for each variable, though variants exist, such as sampling from blocks of variables conditional on all other variables.
On convergence, each full iteration across all variables yields samples from the joint multivariate distribution. As with most MCMC schemes, successive iterates are generally dependent.
It is widely used in Bayesian inference, though it's not limited to Bayesian approaches.