The Gibbs sampler is a type of Markov Chain Monte Carlo (MCMC) simulation that produces a Markov chain guaranteed to converge to a target distribution $\pi$ of interest.
Assuming this target $\pi$ is defined on a space of dimension larger than one, the sampler is based on iterated simulations from the full conditional distributions associated with $\pi$ for each variable, though variants exist, such as sampling from blocks of variables conditional on all other variables. There also exist versions for univariate targets $\pi$ based on completion schemes like slice sampling.