What state transition testing is
State transition testing is a black-box technique for anything whose behaviour depends on what has already happened. An order that has shipped cannot be cancelled the way an unpaid one can. A subscription in its grace period behaves differently from one that has lapsed. The same event produces different results depending on the state, and the test design has to account for that.
The model has four parts: states, events that trigger change, transitions from one state to another, and the actions that happen on the way. It can be drawn as a state transition diagram or written as a state table, and both describe exactly the same thing.