When this spring gets stretched, x changes. There are lots of other variables that describe a system, besides the state variables. Let's name some of these so that we can keep clear which variables are state variables. Consider a spring and a mass. The spring has spring constant k , and we've learned that a simple constitutive law states that the spring will exert a force f which is equal to kx , where x is its displacement from its rest length.
Parameters describe what the system is , while state variables describe what it is doing .
Recall that the state variables are functions of time. These are called initial conditions . But there is no way for us to predict what will happen next if we don't know what the system is doing right now. It could have positive velocity and be moving to the right, or negative velocity and be moving to the left. You can't tell.