A political faction is a grouping of individuals, especially within a political organization, such as a political party, a trade union, or other group with a political purpose. It may also be called a power bloc, or a voting bloc.
The individuals within a faction are united in a common goal for the organization they are a part of. They stick together to achieve this goal and improve their position within the organization.
A political faction could be described as a “party within a party”. But political factions are not limited to political parties; they can form within any group that has some sort of political aim or purpose.