State patterns are directly related to FSMs. An FSM, in very simple terms, is something that has one or more states and travels between them to execute some behaviors. Let's see how the State pattern helps us to define FSM.
A light switch is a common example of an FSM. It has two states--on and off. One state can transit to the other and vice versa. The way that the State pattern works is similar. We have a State interface and an implementation of each state we want to achieve. There is also usually a context that holds cross-information between the states.
With FSM, we can achieve very complex behaviors by splitting their scope between states. This way we can model pipelines of execution based on any kind of inputs or create event-driven software that responds to particular events in specified ways.