The self
A person's self is the subject of a dream in Freud's theory, so that the self can be thought of as the participant of the dream, but he entertains different theories about the other aspects of the dream as if they could be reflections or projections of the same self as a person works through essential dilemmas from their daily life, such as strongly felt, unmet desires, and complicated emotional conundrums.
Family and community
The cast of a dream is frequently one's close relatives and members of one's community, like authority figures (perhaps teachers or police). The frequent introduction of characters that one knows is a strange aspect of dreams, and he suggests that perhaps the involvement of other people in one's dreams could represent emotional homework that the self does to examine emotional situations or dynamics.
Archetypes
Freud also submits a theory that perhaps other aspects of dreams that have "character" feeling to the self are actually archetypes of the self's unconscious design, so that a person might encounter mythical experiences in their sleep that have strange similarities to other human stories with the same shape or dynamic. Perhaps a person encounters a mythic animal, or perhaps they encounter an experience with something sublime, as in many nightmares.