By federal statute (28 U.S.C. § 2) the United States Supreme Court sits at “the seat of government” the first Monday in October, and continues until about June or July. Anyone who has spent a summer in the Washington, D.C. area can understand why, particularly before air conditioning was invented, the Court leaves town during the summer. The Court used to sit in the Capitol (from 1819 to 1935), but in 1935, the current building was completed, with the ornate Corinthian columns and “EQUAL JUSTICE UNDER LAW” motto.
When the October Term commences, two things usually happen. Neither represent a final decision on any case, but both are generally reported as “news”, even though they mean very little.
First, the Court announces whether the writ of certiorari is going to be granted for pending cases. Approximately 7,000 petitions for certiorari (an order granting appellate review, which requires the lower court to "certify" a record of proceedings for review) are filed each year, and only about 100 are granted. Most are culled by the small army of law clerks working for the justices, and then at least four (4) of nine (9) justices have to vote to grant certiorari. A case has to present not only an important issue of federal state or constitutional law, but usually a fairly well developed dispute among the lower courts, the federal circuit appeals courts. Denial of certiorari does not mean approval of the circuit court’s decision, but merely allows it to stand. For example, the Pledge of Allegiance Case, assuming it does not get reversed or withdrawn by the Ninth Circuit, only meets the minimum requirement for review, because it conflicts with a Seventh Circuit case on the same issue. Denial would not mean the Court agreed with the Ninth Circuit: the Court would certainly rather hear from more of the twelve circuit courts before taking up such an inflammatory issue.
The other thing which happens is that the Court begins hearing oral argument on the cases it has selected for review. The Court sits “en banc” (meaning at least six but usually all nine of the justices) hearing 30 minute arguments from each side. Arguments are open to the public, but seating is limited. Argument is frequently interrupted by questions from the justices.