What it is: The power, or the right, of a group or nation to decide how it is governed and what its relationship with other groups or nations should be. There are several reasons why a group or nation may not have this freedom. For example, it may have been been colonised or invaded by another country, or lack the political strength and the economic resources needed to be fully independent.

What it means: Not all groups that want full or partial independence are able to get it, or at least not easily. Larger groups or states in which they are situated will often try hard to prevent them from running their own affairs. For example, Somaliland claimed independence from Somalia, but Somalia (and, so far, the rest of the world) has refused to acknowledge it. The province of Kosovo briefly achieved partial self-government in the 1990s: Albanian Kosovars (most of Kosovo's population and unpopular with the Serbian government) had created their own working system for education and other social institutions. But when a group of Kosovars formed themselves into the Kosovo Liberation Army and began fighting for independence, the government of Serbia responded with force too, driving many ethnic Albanians (who took no part in the fighting) out of their homes. After this war, many Kosovan Albanians began threatening Kosovan Serbs, many of whom felt forced to move out of the province (though it had been their home for generations, too). Another example: East Timor's desire for self-determination was brutally opposed by the Indonesian government, whose troops had invaded the country when Portugal (which had originally colonised it) pulled out. After this bitter and bloody conflict, East Timor finally gained independence, as Timor-Leste, in 2000, and began re-building and working towards reconciliation with Indonesia. Many countries which had been colonised, mostly by European states, began their new life as independent states poorly-equipped for self-government: colonisers didn't usually try to ensure that colonised peoples had the necessary skills and resources to run things themselves. In some cases (when the British left Palestine or the Belgians left Congo, for example) the colonial power's departure was sudden, with little or no time for transition: confusion and violence followed. On the other hand, when the Cold War ended and communism collapsed, no less than 22 self-determining states emerged, and thousands of miles of borders were redrawn. Seldom, if ever, has a highly authoritarian political system, deploying military means sufficient to destroy life on earth, been dismantled so ‘peacefully’. Never has an empire disintegrated with so little bloodshed. Although huge difficulties remained for the successor states. 

Think about it:
Why do people want freedom to choose their own kind of government? How often might this be because they want freedom FROM an existing rule? Why do states tend to feel threatened when a smaller political or ethnic group want to be self-determining? - Russia's response to Chechnya's separatist ambitions, for example. Think about these questions, and work out ideas for resolving self-determination problems without violence. (Note that the dominant state may almost certainly have a professional army, and think about how that alone can hinder a peaceful solution. Think also about the hidden - and complicated - motives and agendas that equally certainly exist on all sides. The country seeking self-determination may have valuable oil and mineral reserves, for example. And what political leaders want, whatever they may say, isn't necessarily what the people want - or need.) 
(2) Is democracy an important factor in self-determination? The Organisation for Security and Co-operation in Europe (OSCE) stated at the time of its foundation that democracy and the rule of law were essential for human rights. Many people continue to believe that democracy is the only way to run communities and states which contain people from a variety of ethnic groups - if only because democracy is the only system we have so far tried out that, in theory at any rate, allows cultural differences to be respected. Yet some activists for self-determination are dedicated to nationalism too - such as the leaders of the Chechen independence movement, or of the Albanian Kosovars. In a self-determined group or state, can everyone's human rights be ensured? If so, how? If not, what possible solutions might be worth trying?