Hyperconjugation effects:

Both of the inductive and hyperconjugation effects are greater while there are three alkyl groups related to the carbocation center than while there are only one or two. Hence, tertiary alkyl halides are far more likely to generate a stable carbocation intermediate than as primary or secondary alkyl halides. It is significant to realize that the reaction rate is determined through how well the transition state of the rate determining step is stabilized. In a condition like this where a high energy intermediate is made (that is the carbocation), the transition state that is leading to it will be closer in character to the intermediate than the starting material. Hence, any factor that stabilizes the intermediate carbocation as well stabilizes the transition state and therefore increases the reaction rate.