Essentially, it is the adjacent atoms or groups attached to the central carbon atom which have the ability to stabilise or destabilise a carbocation. The formation of this carbocation is what determines the rate of the reaction (as the Rate Determining Step), therefore the level of stability of the carbocation intermediate will determine how quickly or slowly this intermediate is formed; a stable intermediate will form quicker than a more unstable one.
Large bulky alky groups possess electron donating (ED) effects, meaning it pushes electron density onto the central positively charged carbon atom through resonance. The fewer ED groups which are attached to the central carbon the less stability will be given to the carbocation via resonance. A general rule of thumb in order of stability: tertiary carbon > secondary > primary. Also important to note that groups such as nitro or carbonyl groups will have the opposite effect as they possess a electron withdrawing (EW) effect.