A trial by battle is a means by which a party can prove their innocence when accused of a crime in the Seven Kingdoms. In lieu of a standard trial where a lord hears testimony from the involved parties and makes a ruling, one or all parties may choose the option of a trial by battle.
In a trial by battle the accused may represent themselves in combat or, if unable (say if they are female or injured), may ask for a champion to represent them. The victorious party is held to have had his or her case judged fairly by the Seven and they are cleared of all charges.
In the books
In the Song of Ice and Fire novels, trials by battle are risky gambits only invoked when there is little other choice. In historical times there were more variations of the trial, such as a trial of seven when the two sides would pick seven champions who would fight until one side yielded or the complainant withdrew their charge. This was held to be a more holy contest, but the practical difficulties have made such trials rare. Ser Duncan the Tall first came to the attention of legend by holding a trial of seven against his accuser, Prince Aerion Targaryen, and defeating him and his force.
For trials by battle involving the royal family, they must be defended by a knight of the Kingsguard.