Of or relating to the upper or middle classes. This term is not generally used by people in the American middle class, and using it may cause the speaker to be identified with the working class. When it's used, it often describes something that is "middle class" or "upper class", with positive connotations.
From Elvis Presley's Hound Dog: "She said she was high class; well, that was just a lie."
A girl with high standards and doesn't sleep around, but rocks mad wheels
Is Alyssa a slut?
Not a chance! That girl is high class!
Of or relating to the upper-middle or upper classes. This can be in reference to clothing, behavior, tastes, pedigree, and more.
Contrary to what low-income African-Americans think, driving a new, clean, shiny Benz is not high class.