When the term first emerged in the 1970s, "the neoconservatives" referred to three overlapping groups:
(a) Scoop Jackson Democrats, such as Jeanne Kirkpatrick, who opposed the McGovern campaign and their party's related drift towards dovishness. Fiercely pro-Israel and pro–Cold War, they pretty much all re-registered as Republicans by the end of the '80s.
(b) ex-Trotskyist New York intellectuals, such as Irving Kristol, who were dismayed both at the aforementioned drift toward dovishness and at the New Left's "barbaric" attitudes toward Israel, higher education, and the old liberal establishment.
(c) formerly liberal academics, such as Peter Berger, whose research led them to reject the case for Great Society programs -- and, in some cases, the case for even larger swabs of the welfare state.
The third group is obviously somewhat different from the first two. It got roped in because its members were reconsidering their liberal or leftist sympathies at the same time as the others and because they often ended up publishing in the same magazines (The Public Interest, Commentary, etc.). Many of their then-controversial claims are now accepted by people who still consider themselves liberal; many of their articles are cited warmly by libertarians who otherwise profess to hate neocons.
If the third group has grown less essential to the definition of neoconservatism, then a fourth group has picked up the slack: second-generation neocons like Bill Kristol, who aren't "neo" in the sense of being former liberals but are "neo" in that their beliefs are in many ways distinct from those of the pre-neocon Right. Confusing matters somewhat, some libertarians and paleoconservatives have attempted to retrofit the word to describe the ex-Communists who seemed to join the Right en masse during the late '40s and the '50s (James Burnham, Max Eastman, etc.), helping turn its attention from limited government at home to an active foreign policy abroad.
Israel is a central foreign-policy concern of the neocons, in many cases the central foreign-policy concern (which is why I get annoyed when critics of Israel, such as Christopher Hitchens, are shoved under the neocon label). In terms of domestic policy, I think David Frum was right to divide the neocon tribe into two groups: the "optimists," exemplified by Jack Kemp, and the "pessimists," exemplified by James Q. Wilson. For the details, read his book Dead Right.
Finally: "neocon" is also an insult that some libertarians like to hurl at other libertarians. If one lib says another lib is "basically a neocon," it's his way of saying the other guy is too hawkish, too corporate, too gradualist, or altogether too close to the establishment.
Everybody got that? Good; there'll be a quiz on Friday.