At the molecular level, kinetic energy determines how fast atoms and molecules move and vibrate. Temperature is actually a direct measure of the average kinetic energy of particles in a substance. When temperature rises, molecules move faster and carry more kinetic energy on average.
This idea forms the core of kinetic molecular theory, which explains gas behavior, diffusion rates, and pressure. Higher kinetic energy also means molecules collide more often and with greater force. Since chemical reactions require molecules to collide with enough energy to break bonds, faster-moving molecules react more frequently and more effectively.
This is one major reason reactions generally speed up as temperature increases. Not every molecule in a sample moves at the same speed, though. At any given temperature, molecules follow a range of speeds described by the Maxwell-Boltzmann distribution, with some moving much faster or slower than the average.
Kinetic energy is closely tied to activation energy, the minimum energy molecules need to react when they collide. Even at a given temperature, only a fraction of molecules have enough kinetic energy to overcome this barrier during a collision. Raising the temperature increases the fraction of molecules with sufficient energy, which is why even a modest temperature increase can significantly speed up a reaction.