Let me address this from my own point of view because you can argue that I am an outsider-within due to racial or ethnic factors.
As a highly educated American citizen, I should be (you can argue) a member of the dominant group in this society. I have a BA from an elite university, and a Ph.D. I have taught at the university level; I should have status.
At the same time, however, you can argue that my ethnicity (mixed race) puts me in a subordinate group. Because of my ethnicity, I have experienced things (family members trying to discourage my wife from marrying me) that "should not" happen to people of my status.
Sociologists would argue that this makes me an outsider-within because I have characteristics of a person from both a dominant and a subordinate group. I'm not sure I agree, but that is the argument.