An outcast is someone who is rejected or 'cast out', as from home or society, or in some way excluded, looked down upon, or ignored. In common English speech an outcast may be anyone who doesn't fit in with normal society, which can contribute to a sense of isolation.
In Ancient Greece the Athenians had a procedure known as "ostracism" in which all citizens could write a person's name on a shard of broken pottery (called ostraka) and later place it in a large container in a public location. If an individual were to have his or her name written a sufficient number of times, they would be subject to "ostracism" and banished from the city for ten years. This was normally practiced against individuals who had behaved in a manner that was in some way offensive to the community.
To be exiled is to be away from one's home (i.e. city, state or country), while either being explicitly refused permission to return and/or being threatened with imprisonment or death upon return. It can be a form of punishment. Exile can also be a self-imposed departure from one's homeland. Self-exile is often seen to be in some way a protest by the person that claims it, to avoid persecution or legal matters ( tax, criminal allegations, or otherwise), through shame or repentance, or perhaps to isolate oneself in order to devote time to a particular thing. Article 9 of the Universal Declaration of Human Rights states that, "No one shall be subjected to arbitrary arrest, detention or exile."
In the Old Testament, Ishmael, the son of Abraham, was cast out after the birth of Isaac, his half-brother, who is considered the forebear of the Israelites. Genesis 16:12 of the Bible prophesies Ishmael's life as an outcast: "And he will be a wild man; his hand will be against every man, and every man's hand against him; and he shall dwell in the presence of all his brethren."