What are Markov chains?

A Markov chain is a mathematical system that goes through transitions from one state to another based on probabilistic principles. The distinguishing feature of a Markov chain is that the potential future states are fixed, regardless of how the process got to its current state. In other words, the likelihood of transitioning to any given condition is completely determined by the present state and the amount of time that has passed.
The math underpinning Markov chains necessitates familiarity with linear algebra and matrices.