This type of motion is known as vibrational motion. Of the three states of matter for a given substance, the solid state has the lowest temperature and therefore the particles have the lowest average kinetic energy or least amount of motion. They vibrate while staying locked in their positions with respect to other particles. As the temperature increases the rate of vibration increases.
Particles in the liquid and gas states have vibrational motion as well, but they also have translational motion. This means that the particles are free to move around as opposed to being in fixed positions. This is why these states are called "fluids" - they flow. Particles in the gas phase have higher average kinetic energy than in either of the other two phases as they are moving at a higher rate of speed.