Andrei Andreyevich Markov is known for his work in probability theory, especially for having explored sets of related states (e.g. in a finite state machine), whose future conditional probability distributions depend only on the current state. Such a relationship is now called the Markov property, and may also be called Markovian.
Many situations can be modeled as having this property. For instance, here is a Wikipedia page that depicts how a Markov process could be used to model expected weather conditions, given the current weather. The page also explains how to calculate a steady state for the Markov process, in order to be able to say the "percentage chance" that a particular day will be sunny.
To learn more about Markov processes, it may help to review this Markov Process Introduction PDF (82k), by Saban Alaca of Carleton University, which provides the essential details about Markov analysis, along with some helpful examples and exercises.
