Most computational methods in engineering have one main goal: to allow you to determine the “state” of something. The question of determining the state only arises if the state can vary. It hurts to say this but the variables that best define the state of the system are called the state variables.
There are often multiple variables you can choose. However, engineers usually look for a Governing Differential Equation or Equation of State that some physicist – or family of physicists – has had the good grace to discover and document. In this case, the GDE or EOS decides what the state variables are. Remember that time can be a state variable too.
This 11 minute video is well worth watching.