Markov process with a discrete state space. More generally it's a chain (a Directed network, where every node has out-degree and in-degree 1, forming a chain) of Random variables that satisfy a Markov property.
Markov Chains explained visually. Nice simulator online
Can have:
Ergodic theorem for Markov chains
Has applications in theory of Stochastic processes, and in Machine learning. In particular through a Hidden Markov model
See also Finite state channel
Order of a Markov chain. See here
Markov subchains A subchain of a Markov chain is also a Markov chain
Regular Markov chain here here
See book Markov chains by Norris