Answer:
The Judiciary Act of 1801 (also called the Circuit Court Act and sometimes the Midnight Judges Act), passed in February 1801, in the waning days of John Adams' presidency, and replaced the original Judiciary Act of 1789.
The Act served two purposes. Ostensibly, it reorganized the federal court system by doubling the number of circuits from three to six and adding five new district courts, in order to relieve the Supreme Court justices of their circuit riding responsibilities. The Act created sixteen new federal judge positions, and gave all Article III judges lifetime tenure. It also changed the schedule of Supreme Court Terms from February and August to December and June, and reduced the number of Supreme Court justices from six to five, because the new appellate courts were expected to lighten the Court's caseload. On the surface, these changes seemed rational, in light of the heavy travel schedule the justices maintained.
The second, and probably more important, purpose of the Act was political.
The matter of greatest concern to the Democratic-Republican members of Congress was that it advanced the Federalists' agenda by shifting jurisdiction over many federal cases from the State courts to the US circuit courts. The Democratic-Republicans believed this weakened the States, but were unable to stop the bill from passing because the Federalist party controlled the Sixth Congress.
Federalist John Adams lost his Presidential reelection bid to Democratic-Republican Thomas Jefferson in the 1800 election. The Federalist party also lost a number of seats in Congress, such that they would no longer control the legislature once the Adams' administration ended. With the Federalists outnumbered in both the Executive and Legislative branches, their only opportunity to influence government was through control of the Judicial branch. The Judiciary Act of 1801 was adopted during Congress' lame duck session, and was considered a bit scandalous because major bills were supposed to be deferred to the next Congress.
The timing of the bill's passage also allowed President Adams the opportunity to select all the new Article III judges, who were guaranteed lifetime appointments ("during good behavior"), and ram their confirmations through the Senate before leaving office. Adams quickly filled all the vacancies with members of the Federalist party.
A second piece of legislation, the Organic Act of 1801, incorporated parcels of land ceded by Maryland and Virginia into the District of Columbia, officially creating the nation's capital and two separate towns, Georgetown, MD and Alexandria, VA, which operated under their respective states' laws. One provision of the legislation allowed President Adams to appoint an unspecified number of justices of the peace to serve the capitol area. Adams nominated another 42 Federalists to these posts. (Collectively, these men became known as the Midnight Judges for their last-minute appointments.)
Adams was accused court-packing for installing so many members of his own party in the federal judiciary. Jefferson and the new Democratic-Republic-dominated Congress thwarted Adams' attempt at monopolization by passing the Repeal Act of 1802 in March 1802, which eliminated the additional judgeships and temporarily resurrected the Judiciary Act of 1789. As a result, the US Supreme Court had no Term in 1802.
Jefferson disposed of some of Adams' justice of the peace commissions by more literal means, an action that precipitated the landmark Supreme Court case Marbury v. Madison, (1803).
For more information, see Related Questions, below.