Regime: A system of government, a way of doing things, the adminstration in control of a country.
The word regime is often used in international affairs (and in propaganda statements) to refer to the rulers of a country when the speaker does not want to dignify them with the title of government or leader.
The implication is that a regime is something that is imposed on the country. They are the ones with power over their subjects, but they are not a legitimate government out of those people. This is usually by virtue of the regime not being democratically elected.
Thus you could hear
The apartheid regime of South Africa was replaced by the ANC government in 1994
or
Our legitimate demand that the Iraqi regime surrender all their alien UFOs was met with a flat denial of any extraterrestrial activity.
See also the euphemism regime change.