The right of nations to self-determination (from German: Selbstbestimmungsrecht der Völker), or with less words, self-determination is the idea that nations have the right to choose their sovereignty (who or what rules them) and international political status without other countries telling them. Most of the world used to be ruled by empires (really big countries with more than one ethnic group, usually with one group having a lot of power over the others), and many of the countries that the empires ruled were considered colonies of the empire, but after The first World War (1914-1919), and especially the second World War (1929-1945), most of these empires collapsed (fell apart) and local populations (people living in the "colonies" native to the area) began to want independence and their country to be ruled by them, not someone very far away who they thought was mistreating them. Lots of nationalist movements arose in these countries, usually in Asia, Africa, and the Middle East, because people usually considered themselves as a separate group than the one who ruled them (for example, Arabs, not British, when the British Empire had ruled a lot of Arabia).
Some people who believe in self-determination use violence, others do not.