State
In most parts of the world, a state is an actor that has a monopoly on the "legitimate means of coercion" within a defined boundary. Until very recently,When? these were considered the only important actors in international affairs. Classic examples of states include Iran, Finland, and (for historical reasons) the United States.
If a state becomes too weak, and loses legitimacy (or other actors gain legitimacy), then it is often called a failed state. The most classic example of this is Somalia.
[edit] State and nation
A state should not be confused with a nation. A nation is a group of people bound by a common culture, history, religion, language, and/or ethnicity. Many nations, such as the Germans or the French, have their own states as well. However, others do not, such as the Basque and the Kurds. Moreover, it is possible to have a state without a foundation in a single nation, as was the case with many of the African states upon independence. One could also argue that Switzerland, with its four languages and religious plurality, could be considered a "multi-national state". A state that is founded upon a single nationality is called a "nation-state." This was the primary means of legitimacy for states in the past, and many of the most stable still rely on it.
Within the United States, the term state also means one of the geographical subdivisions of the US. In theory, each of them independently derives their own legitimacy, but in practice they are merely administrative divisions within the US. Examples of this usage include Kentucky, Tennessee, and New York. This, more than anything else, has led to the confusion about the terms nation and state within the US.
[edit] State and government
In the United States, the terms State (as defined here) and government are used interchangeably. However, in parliamentary systems (e.g., Canada) the government refers to the executive — what in the U.S. is called the "administration." This also leads to confusion, as there is no terminological distinction to be made between the apolitical machinery of the State and the political leaders in the government or administration.