Kinetic Theory of Matter
The kinetic theory of matter states that all matter is made of tiny particles in constant motion, and that temperature measures their average kinetic energy.
Definition
The kinetic theory of matter states that all matter is made of particles in constant random motion, that the average kinetic energy of those particles is proportional to temperature, and that the state a substance takes depends on how that motion compares with the forces of attraction between particles: solids vibrate in place, liquids slide past each other, and gases move freely. More precisely, each particle's translational kinetic energy averages $\frac{3}{2}k_BT$, with speeds spread according to the Maxwell-Boltzmann distribution, and for ideal gases the theory derives the gas laws from elastic collisions with container walls, giving $PV = \frac{1}{3}Nm\overline{v^2}$ and hence $PV = nRT$. Applied to condensed phases, it also explains evaporation as fast particles escaping a surface, the flat plateaus on heating curves where energy goes into breaking attractions rather than raising speed, and diffusion.
Example
Food coloring dropped into water without stirring slowly spreads on its own as moving water particles bump it around, and it spreads through hot water in seconds but takes minutes in cold water because molecules at $80^\circ\text{C}$ move faster than those at $5^\circ\text{C}$; gas pressure comes from particles striking the container walls, which is why heating a sealed can raises the pressure inside. At $25^\circ\text{C}$ the average kinetic energy per molecule is $6.17 \times 10^{-21}\text{ J}$, the same for every gas, so because helium is lighter than nitrogen its molecules move faster ($1363\text{ m/s}$ versus $515\text{ m/s}$ rms) to carry that same energy, which is why helium leaks out of a balloon overnight.
Key Insight
Even a solid rock is full of particles that never stop moving, they just wiggle in place instead of traveling, and temperature measures their average speed rather than the total amount of heat present, which is why a $1000^\circ\text{C}$ spark cannot burn you (too few fast particles) while a $40^\circ\text{C}$ bathtub holds far more total energy. Absolute zero is the temperature at which particle kinetic energy would reach its quantum-mechanical minimum rather than true stillness, and the Kelvin scale exists precisely because kinetic theory shows temperature is proportional to energy, and a proportional scale needs a genuine zero point.