Neoconservatism refers to things that are pro-American nationalist interest in international affairs. This includes bigger military, pro-democracy, nationalism, anti-communism. It started in the United States during the 1960s. Neocons supported the Vietnam war, but disliked the Democratic party, Great Society, and the New Left.
Neoconservative sometimes refers to people who started as anti-Stalinists and then became American conservatives during the 1960s and 1970s.
Examples
Some neocons are Republicans, like the presidents between from the 1970s to the 2000s. For example, George W. Bush started the 2003 invasion of Iraq. His neocon friends include Paul Wolfowitz, Elliott Abrams, Richard Perle, and Paul Bremer. Dick Cheney and Donald Rumsfeld also listened to these neocons. Together they supported the defense of Israel and the American invasion of the Middle East. Very few of those people actually called themselves Neoconservatives though. Some people who call themselves Neoconservatives are Douglas Murray and Reihan Salaam.
Where did it come from? Neocon started in the 60s with Jewish magazine Commentary, edited by Norman Podhoretz and published by the American Jewish Committee. They opposed the New Left and thus started the neocon movement.