What is the only thing that changes in a change of state?

That is really hard to answer... There is no ONE thing that changes when a change of state occurs because one thing leads to another... If I had to give one answer, I'd have to say energy changes.

When a atom or molecule changes state, it can gain energy (liquid to gas or solid to liquid for example) and the bonds are stressed (more of a springy effect) between the protons to electrons as well as covalent and ionic bonds. So the stability decreases while the size of the element or compound increases.

A good example of this is leaving a water bottle outside in the sun. The sun adds energy to the water, making it turn into a gas, the gas increases the pressure inside the bottle, thus making the bottle expand.

*If you think about frozen water expanding the bottle it will trip you up. Water is special in that it expands when it freezes as well. I can't think of a common example for expansion right now other than water.*

The electrons/ "vibrations" of the atoms also increase in speed.

When they lose energy (gas to liquid, liquid to solid), the size decreases as does the speed of the electrons/ vibrations. Hence why absolute zero has no electron movement at all. Generally this also strengthens the bonds of the compounds because the bonds are not as stressed. They are more stable.

So, simple one word answer? Energy.