Sanhedrin refers to any and all law courts of ancient Israel. The Great Sanhedrin (which is what is usually thought of when the word "Sanhedrin" is batted about) convened in Jerusalem in the Chamber of Hewn Stone. It existed between circa 57 BCE until the abolishment of the rabbinic patriarchate in about 425 CE.

The Great Sanhedrin consisted of 71 members, including the president, called nasi (lit. "prince") and a vice president called av bet din (lit. "father of the court"). The group was divided into Chief Priests, Scribes, and Ancients, representing those versed in matters of law, The Law, and life, respectively.

The Great Sanhedrin had the powers equivalent to a Supreme Court. It was appealed to when lower courts were unable to come to a particular decision. It dealt not only with legislative and civil laws, but also with religious matters, such as the intricacies of the Torah and ritual law. The Great Sanhedrin reserved exclusively the right to make judgements in matters of special importance, such as the case of a false prophet (recall that whole Jesus fiasco), accusations against a high priest, the deployment of army troops, and ect. Their jurisdiction seemed to encompass all areas not claimed by the Roman authority.

The decisions of its judges were held to be inviolable; a scholar who went against it rulings was put to death as a zaken mamre (rebellious elder).

Criminal cases were tried before a commission of 23 members. In these cases, the younger members were the first to give their opinion. For an acquittal, a majority of one vote was enough. For a condemnation, a two-vote majority was required, except when all 71 members of the court were present.

Interesting lil'factoid: In 1807 Napoleon appointed a "French Sanhedrin" of 71 members, made up of both rabbis and laymen, to consider the relationship between Jews and the state.


Sources:
www.us-israel.org
www.newadvent.org
www.encyclopedia.com

cf. Jewish Sects and Orders