Give that the question is posted in the literature section, I am assuming that the question is meant to refer to a character's failure to feel as though they belong. Essentially, many external factors can force a person to feel as though they do not belong.
These external factors can be defined as external conflict (man verses man, man verses nature, and man verses supernatural). Typically, the conflict of man verses man is the one which causes a character to feel isolated, alienated, and exiled.
For example, a person may not feel like they belong based upon interpersonal conflict. The character may fight with others, be told that they do not belong, or feel out of place in the society as a whole. This comes from the feeling that the character does not share any characteristics of those around them.
As strong as a person may be, the external forces which come into play can have a great impact upon them. For example, if a person (or character) is repeatedly told that they are worthless (as seen in David Pelzer's A Child Called It), they will begin to believe that they are worthless.
Another example can be seen in Laurie Halse Anderson's novel Speak. Melinda, the protagonist, has called the cops on a party she was raped at. No one knew what happened to her because she did not tell. Instead, the entire school only thought she called for no real reason. The entire school turns against her.
IN the end, the external factors which come into play in a character's life can be overwhelming. These factors can, unfortunately, define a character and make them feel as though they do not belong at all.