The study of government and politics, often called political science, is a broad and diverse topic, spanning many interlinking areas. Typically defined as the way in which groups of people make collective decisions, the study of politics delves into much more than simple collective decision making.
The study of politics is essentially the study of our collective mentality. Place one man alone on an island and he will make individual decisions of his own accord with one motive - the need to survive. Place a group of people alone on an island and the scenario becomes infinitely more complex. Immediately, personalities will clash, ideologies will conflict, and sides will be taken. Politics essentially involves studying "mob mentality" and how a small group can govern a much larger group; it is in fact an area of applied sociology. Are all men equal? Should we all be taxed in equal amounts? What punishment and rehabilitation should be implemented to deal with those who break our collective laws? Who is qualified to create and enforce these laws?
These infinitely complex questions make up the core of any government and politics course. Understanding the wider picture and appreciating the moral and ethical factors that influence decision making will play a key role in understanding how the political spectrum works and is divided. As Julius Caesar famously stated: “What we wish, we readily believe, and what we ourselves think, we imagine others think also."
The role of politicians and leaders is not at all a simple one. To help gain a basic understanding of government and politics we recommend starting with MIT's OpenCourseWare called Foundations of Political Science. A more specific source of information would be BBC Politics.