The Supreme Court of the United States is the country's highest court. There is no appeal from a SCOTUS decision. If you win at the Supreme Court, you win. If you lose, you lose. There is no further court to ask. Other branches can sometimes change the situation through new laws or constitutional amendments, but as a matter of judicial process, SCOTUS is the end of the road.
The Court has nine members called Justices. One is the Chief Justice of the United States, the other eight are Associate Justices. They sit in the Supreme Court Building in Washington, D.C., across the street from the Capitol. They serve for life, or until they retire, resign, or are impeached and removed from office. Impeachment of a Justice has happened exactly once in American history and that Justice was not removed, so in practice "for life" means until they choose to leave or they die.
The Court was created by Article III of the Constitution, but the Constitution does not say how many Justices it must have. Congress sets the number. The first Court in 1789 had six members. It has been nine since 1869. There are occasional proposals to add more, often called "court packing" proposals, but the number nine has held for over 150 years.
The Court hears cases between October and June or July each year. This is called the Court's "term." A term is named for the year it begins, so the cases decided in spring 2024 are part of "October Term 2023" or "OT 2023." That is why you sometimes see two years on a case.