As the other responder points out you use state machines everyday without knowing it. A "State Machine" is a mathematical abstraction (i.e. a "computation" mod

As the other responder points out you use state machines everyday without knowing it. A "State Machine" is a mathematical abstraction (i.e. a "computation" model) for the workings of a concrete machine i.e. A real Computer running a Program. When you start to write your programs as state machines you make its operations explicit, unambiguous and clear thus greatly reducing errors and guaranteeing "correctness". This is what makes it "essential". I highly recommend studying Michael Sipser's Introduction to the Theory of Computation to understand this and other computation models (any edition will do).