A nation is a group of people with a shared identity and common history. It is usually (but not always) defined by homogenious ethnicity, culture, customs, language, religion and a mythical homeland or point of origin. Examples include the American Indian Nations and the Jewish Nation.
When a nation and a state share the same geographic area they are referred to as a nation-state. For example, Israel is now a nation-state because of the actions of the United Nations in 1948 to give their people the land in the Middle East.