A StateDiagram visually shows the possible states a node of an abstract machine may go into, and the possible transitions among states. Heavily used in all application areas that use FiniteStateMachines, such as electronics (where such are used to e.g. design PLAs), and the theory of grammars.
It has recently seen more widespread use in software due to its incorporation into UnifiedModelingLanguage, where the machine undergoing transitions is an object of a class.
From ScottAmbler's site "Modeling Style" http://www.modelingstyle.info/