The legal system in the United States is an example of one that is adversarial. In an adversarial system, there are generally three distinct parties in criminal and civil matters. There are the two opposing sides, in which one is often the accused and the other is the accuser. Then there is the decision maker, who is generally a judge or jury.
This type of system dates back centuries to old English law, and the model was imported to America when the land was divided into colonies. The system has greatly evolved over time. In the beginning, for example, those who were accused were not allowed to properly defend themselves. Justice was a matter of having evidence presented in support of the charges against a person and having a decision maker pass judgment.
Under the modern system, legal proceedings usually involve the opposing parties approaching matters in a competitive way. Each of the adversaries is given an opportunity to present arguments and evidence that supports its claims. The adversaries are generally also given the opportunity to question one another.
Allowing this balance of opportunity between the opponents is believed to be in the best interest of justice. It can give the decision maker access to more information than she is likely to receive from either party solely, and it also adheres to a person's rights to defense. The decision makers are supposed to be free and impartial, which generally means that their decisions should not be driven or influenced by any factors other than those strictly related to the matter at hand.
Winning in an adversarial system can be achieved in more than one way. Since the system is based on adversity, when there is none, a matter is generally resolved. This means that if one party concedes to the claims of the other, the challenge ends. A good example of this is the high number of plea bargains that exist in the US. Since the accused agrees to the charges against him, there is no need for the two sides to argue before the decision maker.
In other instances, when the two adversaries remain opposed, it is a matter of convincing the decision maker. To do so, the parties can prevent various types of evidence including testimony, witnesses, and physical items that support all or part of an argument. Strategies that are used include cross examination and closing remarks. Whatever the decision maker decides should be based on what has been presented and not personal beliefs or intuition.