Which is the most important factor in determining the state of a substance?

The most important state in determining the state of a substance is temperature. This is because the kinetic energy of a substance's molecules depend on its temperature. For example, an increase in temperature speeds up the movement of molecules. A decrease in temperature slows down the movement of molecules.

This is important because by increasing or decreasing a substance's temperature, you are also adding or removing energy from it. And when a substantial amount of energy has been added or removed, a substance can change its state from solid > liquid > gas or the other way around.