The suffix "-ern" makes the word "North" into an adjective. An adjective describes a noun. The word "North" is a noun. It is a thing. That's why you might put a "the" in front of it sometimes, i.e. "In the north, we wear warmer clothes."
When you say Northern Taiwan, you are describing the part of Taiwan in which you live.
I would just like to add to what others have said that the noun is almost invariably used in names of areas that have clearly marked geographical confines - in other words the names of countries and continents, for example: North Korea, West Germany (no longer exists), South America.