Most of the time it's something light or unimportant or humurous being referred to, but sometimes it is said solemnly. I noticed that other ethnic groups and minorities do this as well, but have no idea if straight up White people do this.
I know that Italians and Irish people refer to themselves and people whose families have come to the US within the last 3 or so generations.
The Medditerrean and Eastern Bloc has alot of self-referential humor.
Bur what about people who are just White American?