Jeane Kirkpatrick is significant because she was one of the "neoconservative" thinkers who pushed the US towards conservatism in the 1970s and 1980s. She was an important thinker in bringing about the "Reagan Revolution" that transformed the US political scene.
Kirkpatrick's focus was mainly on foreign policy. She believed strongly in opposing communism around the globe. Specifically, she believed that the US should side with any regime that was anticommunist, no matter how repressive it was. She believed that repressive and dictatorial regimes could be brought around by the example of the US and become democratic.
Kirkpatrick ended up as an advisor to Ronald Reagan, as a member of his National Security Council, and eventually as the first woman to be the US Ambassador to the UN.