Political science is a branch of the social sciences that is mainly practiced in the United States and United Kingdom. It is the analysis, description, and prediction of political behavior, political systems and politics. Another way of describing this field is calling it "what politicians study in college." Like the other social sciences, it's considered a "soft" science, meaning it revolves more around subjective interpretations than hard data. Due to the complexity of human behavior when it comes to politics, it will be a long time before it can be anything else.
The object of political science courses is to groom students for careers in politics, or to give them an awareness of the political process that might be useful in some other career. Politics is complicated, both in terms of the rules and the strategies to be used.
The field as a discipline is relatively recent, with the name popping up in America immediately after the Civil War. The name quickly spread to the UK. Although universities around the world have political courses, they tend to lack the scientific flavor of "political science" courses specifically.
Political science has clear antecedents stretching back to ancient civilizations: moral philosophy, political philosophy, political economy, history, and so on. Clearly, many of the leaders of history were aware of the ins and outs of politics, although circumstances tended to be more chaotic, and military prowess alone may have been sufficient to gain control of a nation or empire. With the more recent establishment of stable states and the suppression of corruption, politicians have had more incentive to work within the system as it exists, leading to this discipline.
One of the most influential works in the field is probably The Prince, written by the Italian diplomat Niccolo Machiavelli in 1513. The book puts forth strategies for a leader to establish a strong empire in the face of various challenges. The main argument is that while a leader should publicly seem good and just, behind the scenes it may be worth taking underhanded actions to achieve political goals. This argument has led The Prince to also be one of the most controversial political books of all time.