Markov chains are directed graph
s, the nodes
of which represent possible state
s of the world; the arrows
represent possible transitions
between states; probability value
s are attached to each transition, the probability of that transition occurring when in that state.
The purpose: given a Markov chain you can compute the probability of the world being in any given state.
(Assuming the validity of your state diagram model, of course.)
See also: finite state machines/finite state automata, Petri nets.