The American system of criminal prosecution is an accusatorial system, meaning the government, after accusing the defendant must prove its allegations by an adversary process. An adversary process is one in which each side (the prosecution and the defense) presents its most persuasive arguments to the judge or jury.
For example, the prosecution presents facts that support its case and points out weaknesses in the defendant's arguments. The fact finder (the judge or jury) then decides the case based on the evidence that has been presented. Accusatorial system is the same as adversarial system.