Nationalism, broadly speaking, is the belief that one's country is great, often bundled with the idea that your country will be better off acting independently rather than engaging in international alliances.
Hypernationalism is often used to refer to a strain of nationalism in which one also holds that other nations are both inferior and threatening. This generally involves some racism or xenophobia, a push to build a strong military, and lots of angry rhetoric. It is generally not a good sign for continued regional peace.
There is an unfortunate trend to refer to hypernationalism as simply nationalism, which has the effect of characterizing fairly inoffensive people as rather more problematic than is warranted, and further blurring the already fuzzy line between patriotism and paranoid nuttery.