What is the significance of combining "Gangnam" with "Style"?

Solution 1:

From Today I found out

“Gangnam” is an area in South Korea, specifically a small area in Seoul, South Korea, home to about 1% of the population of Seoul and is about the size of Manhattan. It is known for its wealthy “new money” inhabitants.

“Gangnam Style” simply is referencing this sort of elite, “new money”, wealthy culture and lifestyle that has sprung up around the region. Pop critic Kim Zakka, who lives in Seoul, said “Gangnam inspires both envy and distaste. Gangnam residents are South Korea’s upper class, but South Koreans consider them self-interested, with no sense of nobility.”