When used in a sentence such as: "What the hell do you think I am anyway, chopped liver?!" it shows a person's amazement and feeling of being offended by not being regarded highly or importantly enough.

While rooted in Yiddish or Jewish culture, this expression was actually coined in America. Chopped liver is most often only served as a side dish and so if one feels that one is being overlooked or put aside, one can ask if one is chopped liver.

How that actually makes any real sense I have no idea.

Why did I bother to look it up and eventually write about is? Because of the new Eminem song "Without Me", particularly the part where he sings:

I created a monster, cuz nobody wants to
See Marshall no more they want Shady
I'm chopped liver