Rate of reaction is determined by the number of successful collisions between the reactants per second. A collision is successful if two particles collide with enough energy to react. This can be affected by temperature or concentration (pressure of a gas).
When a substance is heated, the particles gain kinetic energy. This means they will move faster and so collide with more energy, meaning that the collision is more likely to be successful. Increasing the concentration means there are more particles in an area, so they are more likely to collide as they move and therefore there will be more successful collisions per second.