"1st generation" refers to the foreign-born immigrants. "2nd generation" refers to the first native-born generation.

This is the official bureaucratic definition and they're fairly straightforward.

The thinking that just because someone is foreign-born, they cannot be considered American has tones of jingoism. And the idea that someone must be citizen to be an American ignores the fact that immigrants and women were long barred from citizenship. You're American the moment you settle on these shores - you're not a citizen, but you're living in the culture, land, and ideals of the USA. It can't be helped.