What property of matter does temperature measure?
The particles' average kinetic energy.
This is a funny question because temperature is a property of matter - a physical property to be exact. This includes the temperature points of changing states - boiling, melting, and freezing points.
In terms of matter itself, temperature is directly proportional to the average kinetic energy of particles.
If you add energy to particles - heating the object up, you are increasing the object's temperature. As a result, the object will eventually change state where the particles are able to "fly" past one another.
Hope this helps :)