An outcast is someone who isn't wanted. To remember what outcast means, flip it around: outcasts have been cast out from somewhere.
No one wants to be an outcast: such people are rejected by their peers. We all feel like outcasts sometimes. For example, if no one wants to sit with you at lunch, you will probably feel like an outcast. There are much more serious cases too: if a person is thrown out of a community or country, they are considered an outcast (or an exile).