Nations are countries with governments etc. Simple examples of these are the United Kingdom, the USA, every country in the world.
Often national boundaries are drawn using the geography as a rule of thumb ... completely ignoring the ethnic, religious and cultural make-up of a region. The mayhem caused by the above is best described by the terms ethnic cleansing, religious war and extreme shittiness. Examples of this are the Balkan states, Iraq, most African countries, Ireland/Eire and North/South Vietnam till they were ...errr... 'unified'.
Nations also need not have a government except in name. Somalia (civil war), Congo (more civil war), Zimbabwe (Fcuk knows what you call this mess) for example.
Sometimes nations can be partitioned at the 'insistence' of an invading nation ie Germany after WW1 (Alsace Lorraine - French demands), Germany after WW2 (east/west Germany - Russian demands), Cyprus (Greek and Turkish - just keeping them apart)