Markov chains are
directed graphs, the
nodes of which represent possible
states of the world; the
arrows represent possible
transitions between states;
probability values 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.