The Federalist Society for Law and Public Policy Studies is an organization of lawyers and law students in the United States. It started in 1982 with chapters at Harvard, Yale, and Chicago; nowadays, the Federalists can be found in just about every law school in America, and in every major city.
They are often described as "conservative," although that's hardly a fair characterization since "conservative" doesn't mean anything any more. Most members are better described as libertarians. Most are fans of Reaganomics and opponents of Big Government. On social issues, the Federalists are very much a mixed bag: there are evangelical Christians within their ranks who believe in the illegalization of abortion and the teaching of intelligent design, and there are also "moderates" (read: plutocrats-to-be) in their ranks who shudder at the blurring of the line between church and state. While most Federalists are Bush voters, you probably wouldn't have trouble finding Democrats among them.
Probably due to its modicum of ideological diversity, the Society doesn't have any opinions of its own. Rather, it serves as a discussion forum and think tank for people with leanings toward the economic right. While the current co-chairs of its Board of Visitors are Robert Bork and Orrin Hatch, both well-known as leaders of the deep right wing, Federalist Society events often host libertarian speakers, and discuss topics such as abolishing federal agencies or reforming tax regimes.
Some have described the Society as a "farm system" for right-wing lawyers and judges. Many Federalist Society members have been appointed to positions in the federal government under the Reagan administration and both Bush administrations. Many judicial appointees of all three administrations have been picked from Federalist Society membership or through Federalist Society contacts.
John Roberts, appointed Chief Justice of the United States by George W. Bush, apparently had a leadership position at one point but denies ever having been a member.