When we use the term "regime" in regular life, we tend to use it to refer to a particular government.  We talk about the need to bring about "regime change" in Iraq, for example.  In international relations, however, the term has a different meaning.  An international regime is not an international government.  Instead, it is a set of rules or expectations that has been agreed upon by some group of international actors (like states).  These rules or expectations are meant to govern or to affect the way states behave in a particular issue area.  A leading theorist (see the beyondintractibility.org link) in this area defines an international regime as a set of

implicit or explicit principles, norms, rules and decision-making procedures around which actors’ expectations converge in a given area of international relations.

This means that an international regime can be something like the Kyoto Treaty on global warming or a treaty that deals with how fisheries will be managed.  It is just a set of rules that have been agreed upon that will affect the way states act in a given area of international relations.