Gangnam is a particular district (or suburb) in Seoul, which is known for it's expensive real estate. I'm pretty sure PSY explained it as "the Hollywood of Korea". 'Gangnam Style' literally translates to 'from the style of the Gangnam area'.
(Making what PSY said on Ellen make more sense, "Dress classy and dance cheesy.")
So the lyrics "Oppan Gangnam Seutail" mean "I am from the Gangnam Style"
Talk To Me In Korean do a very in-depth explanation, if you're interested check it out: (http://www.talktomeinkorean.com/lessons/kpop-psy-4/)