The Collaborative International Dictionary of English v.0.48:

Markov chain \Mark"ov chain\, n. [after A. A. Markov, Russian
   mathematician, b. 1856, d. 1922.] (Statistics)
   A random process (Markov process) in which the probabilities
   of discrete states in a series depend only on the properties
   of the immediately preceding state or the next preceeding
   state, independent of the path by which the preceding state
   was reached. It differs from the more general Markov process
   in that the states of a Markov chain are discrete rather than
   continuous. Certain physical processes, such as diffusion of
   a molecule in a fluid, are modelled as a Markov chain. See
   also random walk. [Also spelled Markoff chain.]
   [PJC]

WordNet (r) 3.0 (2006):

Markov chain
    n 1: a Markov process for which the parameter is discrete time
         values [syn: Markov chain, Markoff chain]

The Free On-line Dictionary of Computing (30 December 2018):

Markov chain

    (Named after Andrei Markov) A model of
   sequences of events where the probability of an event
   occurring depends upon the fact that a preceding event
   occurred.

   A Markov process is governed by a Markov chain.

   In simulation, the principle of the Markov chain is applied
   to the selection of samples from a probability density
   function to be applied to the model.  Simscript II.5 uses
   this approach for some modelling functions.

   [Better explanation?]

   (1995-02-23)