First of all, let us note that NATO still exists. Its purpose is less clear since the end of the Cold War, but it still does exist.
NATO is and was the acronym for the North Atlantic Treaty Organization. This was an alliance that was created in 1949. The point of the alliance was to make it clear that all of the countries in NATO stood together against the threat from the Soviet Union. The original members of NATO were Belgium, the Netherlands, Luxembourg, France, the United States, Canada, Portugal, Italy, Norway, Denmark, Iceland and the United Kingdom. The treaty that these nations signed obliged them to consider an attack on anyone of them to be an attack on them all. In other words, they were to provide collective security for one another. The clear target of this guarantee was the Soviet Union; the countries were setting themselves up as a united bloc to oppose the Soviets and their satellites.
Since the Cold War ended, NATO does not have a clear purpose. However, it continues to exist and has involved itself in such things as the wars in Iraq and Afghanistan and the recent revolution in Libya.