To understand what a regime change is one must first understand what a regime is. The word comes from the French phrase ancien régime or old order, which was used during the French Revolution to refer to the hated Aristocracy. The word, soon after, found its way into political vernacular, meaning the way that things are governed or the standard rules for ruling. In the United States, a regime was established with the adoption of the Constitution. Quite a few things have change a since 1787, but for the sake of argument, this setup the regime of the United States.
A regime change, then, is an illegal modification of these rules. It is illegal only because if it were a legal change the original regime would still be in place. For instance, there are rules for changing, or amending, the Constitution. As long as these rules are followed it is merely a change to the regime instead of being a regime change, a subtle difference but important nonetheless.
Though the literal definition of this word is neither positive nor negative it is commonly used in a negative context for propaganda purposes to instill the feeling that a government is corrupt or unstable and in need of change. I used the phrase "regime of the United States" which isn't something a lot of flag waving American patriots would use. Instead phrases such as "fascist regime" or "democratic regimes in Latin America" make more sense. Obviously the United States is a democratic regime yet we choose to refer to it as a democracy and refer to the corrupt Latin American democracies as regimes.
Another propaganda tactic is to use the word to refer to a person in power, such as the Castro regime, the Noriega regime, the Milosevic regime, or the Hussein regime. This truly is an improper usage of the word. One could not properly refer to the United States as the Bush regime because he was place in power legitimately (for the sake of argument, please don't send me messages about dimpled ballots in Florida). Even though the figurehead changed the regime is the same as it was with Clinton, Reagan, Carter, etc.
A regime change can come about in several different ways. In eighteenth century France, the most prominent and obvious regime change in history came about through revolution, as it did in the Colonial America and Provincial Russia. Also, one can come through an occupation. A good example of this is the colonization of Africa and the Americas as well as the occupation of Japan and Germany after World War II. Furthermore, a regime change can come from a coup d'état, or an assassination and seize of power. The United States has been doing this avidly over the last fifty years in Guatemala, Cuba (although it failed), South Vietnam, Panama and most recently Afghanistan and Iraq.