In a nucleophilic substitution reaction, when the heterolytic cleavage of the bond between the carbon and the leaving group occurs, the leaving group takes the electron pair with it, leaving the carbon center with a positive charge. This electron-deficient substrate is called a carbocation.

In a carbocation, the carbon atom is surrounded by six electrons in the form of three σ bonds, each at an angle of 120° from the other. The carbon is sp² hybridized with a trigonal planar geometry and an unhybridized empty p orbital.

Because the vacant orbital of carbon can readily accept electrons from different nucleophiles, carbocations act as strong electrophiles in chemical reactions.

The simplest carbocation is the methyl cation in which three hydrogen atoms are bonded to the electron-deficient carbon atom. 

Alkyl groups can substitute for the hydrogen atoms to give different types of carbocations. Depending on the number of such alkyl substituents, carbocations can be classified as primary, secondary, and tertiary carbocations.

Alkyl branching stabilizes the carbocation through the inductive effect and hyperconjugation.

The effect is inductive when electron-releasing alkyl substituents donate electron density to the positive carbon center through σ bonds, thereby stabilizing the carbocation.

Increased alkyl substitution increases the inductive effect in carbocations, which consequently increases the stability of the carbocations.  

The stability is further enhanced through hyperconjugation, which involves the overlap between the carbon’s empty p orbital and a suitably aligned filled sp³ orbital of an alkyl group.

With an increasing number of alkyl groups, the effect of hyperconjugation increases, and along with it, the stability of the carbocations also increases.