How does temperature affect reaction rate?

Without getting into complicated calculus, simply put, molecules have to collide in order to react, and they also have to react with so much kinetic energy to react as well (often called the "activation energy"). Remember that temperature is the average kinetic energy of molecules. Therefore, since it is an average, some atoms have sufficient kinetic energy to react, while others do not. Increasing the temperature (or average kinetic energy) means that more of the molecules will have sufficient kinetic energy to cause a reaction, meaning these reactions will happen more frequently. In summary, increasing temperature increases reaction rate.