Extrinsic semiconductors have dopants that dissatisfies the Octet rule. This dissatisfaction allows more mobilization of electrons during electrical conduction processes.
An intrinsic semiconductor that we all know is a silicon semiconductor. It is also known that an ideal and perfect silicon crystal lattice will be very much stable because of the satisfaction of the Octet rule as a consequence of its 4 valence electrons. However, the stability of a silicon lattice does not allow much electrons to participate in conduction since again, there are no excess electrons; almost all electrons are covalently bonded between silicon atoms.
The difference between an intrinsic and extrinsic semiconductor is that intrinsic semiconductors are pure while extrinsic semiconductors are not pure. Extrinsic semiconductors are injected with impurity atoms also called as dopants. These dopants disrupt the stability of the lattice d of intrinsic semiconductors. These dopants must have valence electrons that are greater than 4 (forming a n-type extrinsic semiconductor) or less than 4 (forming a p-type semiconductor). These dopants either introduce more electrons or "holes" that allow mobilization of electrons. A semiconductor with more electrons that can participate in conduction is preferable.
For example, if a silicon lattice is doped with phosphorus (valence 5), the covalent bond between phosphorus and silicon will have 1 excess electron that can participate in electrical conduction processes. Also, since phosphorus has more than 4 valence electrons, a SiP semiconductor is a n-type.