How are carbocations generated?

Carbocations are generated when one of the bonds previously shared by a carbon atom is broken (such as to a hydrogen or halogen atom), leaving it with an incomplete octet. Carbon needs eight valence electrons to have a full octet, and adopts a #+1# positive charge when it shares only six.

Consider this #S_N1# mechanism for the reaction between ( R )-2-idodopentane and methanol.

The leaving group (iodine) leaves with its bonding electrons, resulting in a carbocation as carbon now shares only six valence electrons. The electronegative oxygen atom of methanol will then attack the electrophilic carbocation, attracted to its positive charge (methanol is the nucleophile).

I've chosen not to show stereochemistry in the product, as both stereoisomers (inversion and retention of original) will be present in the product mixture. Also note that another methanol molecule will deprotonate the methanol which initially attacks the carbocation, which is why we end up with a neutral #O# atom without any hydrogen.

The formation of a carbocation can allow for rearrangement to take place in reactions, resulting in more stable products. In this case, the most stable product by #S_N1# mechanism has already been formed (#2^o#).

Though this is an important concept discussed in organic chemistry and relevant to many types of reactions, I have used only the #S_N1# mechanism as an example. This is by no means the only reaction mechanism that the formation of a carbocation is relevant to (unimolecular elimination, addition, etc.).