Social scientists often look at the world through the spectacles of a particular ideology, or belief system. This makes a very complex world easier to understand. It also provides a framework for students to learn about the social and political world and the theories that have influenced people's thinking. Both the functionalist and conflict theories have their adherents and both have something to offer in trying to understand politics and even decide political allegiance. These theories not only address the world of politics, but also many other areas of life, including, crime, education and economics.
Look at the functionalist theory: It sees a world in which everything has its purpose, allowing harmony to reign, most of the time. A functionalist, would claim, for instance, that the existence of poverty and low-paying jobs can act as an incentive for people to work hard and achieve.
Contrast this with how a conflict theorist views the world: The upper and middle classes are perpetuating the existing system, because it suits them to be at the top of the pile. It is only, according to this theory, when the oppressed reach their breaking point and revolt, that change occurs.
Compare the way proponents of each theory view the education system. The functionalist would argue that the system needs blue-collar workers as much as it needs professionals. The proponent of conflict theory would counter by saying that the difference between the education offered by private and state schools is such that it perpetuates inequalities in society.
Contrast the functionalist and conflict theories of crime. The functionalist would argue that those who transgress are usually dealt with by the law and that order is restored. The conflict theorist would argue that the law enforcement system perpetuates the inequalities and would give the example of how many white-collar crimes go unpunished.