Gangnam is most well known by foreign visitors as its the primary business district in Seoul. If you're here on business there's a likelyhood your meetings and hotel will be in Gangnam.
As others have also said, its one of the most wealthy districts, with shopping streets, malls, good restaurants, bars and nightclubs. Psy also popularised the area internatiinally with his YouTube hit 'Gangnam Style'.
The 'Gangnam Look' is also a topic of discussion. It comes from the fact that many Gangnam girls look the same, having undergone similar cosmetic surgery procedures... yes, I'm being serious.
I work in Gangnam because its the most cinvenient for meetings, but almost never go there outside work as it's a concrete and glass jungle. The traffic is also the worst in Seoul.
If you're passing through Seoul Gangnam may be a point of interest to soak up the atmosphere of one of the world's largest and busiest cities and if you're here on business I'd recommend a Gangnam hotel.