A Markov chain is the characterization of a system that transits from one state to another, in a chainlike manner. It concerns any random process endowed with the Markov property: i.e., the property, simply said, that the next state depends only on the current state and not on the past.
It is a Markov model, named for Andrey Markov, for a particular type of Markov process in which the process can only be in a finite or countable number of states. Markov chains are useful as tools for statistical modeling in almost all fields of modern applied mathematics.