Is it their high level of intelligence? Or is it something much more simple, yet profound?
While a cultured person may very well often be intelligent, intelligence alone does not make one cultured. Culture embodies much more than just knowing something; it is founded upon knowledge acquired by such things as being an eclectic reader, or someone who is not only intrigued and influenced by the arts, but who is open minded and non-judgmental.
Moreover, a cultured person is someone who is humble, sincere, respectful, compassionate, and mindful of the universe around them.