In Jung's writing, the Animus and Anima are personifications of the shadow self- the parts of us that for whatever reason, we have prevented from entering the conscious realm.
Each manifestation of the shadow self can represent light or darkness. So when we ignore it and refuse to integrate its qualities, it becomes larger, grotesque, terrifying- both in our dreams and to the people in our every day lives.
If, on the other hand, we welcome the shadow, "the ego will then find an inner power that contains all the possibilities of renewal."
If a man [or woman?] devotes himself to the instructions of his own unconscious, it can bestow this gift [renewal of life, creative elan vital, a new spiritual orientation], so that suddenly life, which has been stale and dull, turns into a rich, unending inner adventure, full of creative possibilities.
Their purpose is to build a bridge to the Self, and when the Shadow and the Self become integrated, it becomes a friend and guide who tunes the Self into higher principles of a more spiritual timbre.
The animus shows up in women when they have an underdevelopped aggression and assertiveness, when they refuse to own their power. In folk tales and cultural archetypes, he can manifest as a death demon, a robber, murderer, or wild animal, like in Beauty and the Beast (where the love of the girl redeems the monster, a metaphor for her animus becoming transitioning from unconscious to conscious). When ignored, he shows up in the way she speaks about certain matters.
One of the favorite themes that the animus repeats endlessly in this kind of woman goes like this, 'The only thing that I want in the world is love -- and he doesn't love me'; or 'In this situation, there are only two possibilities- and both are equally bad.' (The animus never believes in exceptions.) One can rarely contradict an animus opinion because it is usually right in a general way; yet it seldom seems to fit the individual situation. It is apt to be an opinion that seems reasonable, but beside the point.
The convictions of the animus echo the woman's father, and don't seem to take into account the current, particulars of the woman's reality.
As a counterpart, the anima shows up in men when they haven't gotten in touch with their sensitive, artistic, intuitive side. Its appearance in dreams comes as a witch or sorcoress, a murderous Geisha, or some kind of femme fatale; in Medieval Europe, she was the damsel in distress. When men have integrated the anima in a healthy way, he's receptive to qualities typically associated with the female, "vague feelings and moods, prophetic hunches, receptiveness to the irrational, capacity for personal love, feeling for nature-- and last but not least, his relation to the unconscious. When he ignores her, however, she manifests in moodiness and crankiness, and ultimately poor life decisions.
... His anima will often express itself in irritable, depressed moods, uncertainty, insecurity, and touchiness.... These 'anima moods' cause a sort of dullness, a fear of disease, impotence, or of accidents.
As with all aspects of the shadow, they can be projected, and there are certain types of women who seem to be recipients of this kind of projection, "women who are of 'fairy-like character especially attract such anima projections, because men can attribute almost anything to a creature who is so fascinatingly vague and thus proceed to weave fantasies around her."
Men afflicted by the anima can "fall in love" with a woman on a dating site without ever meeting her because he recognizes his own anima within her, and becomes helplessly attached to her picture and her profile (obviously women can do this too, by the way.) Men who cling onto lost or former lovers - sometimes for years- can seem to the woman like a leech sucking the life out of her, draining her energy, living off her femininity (and vice-versa for women clinging to former lovers). A simple way to solve this problem is to understand the anima as a source of inner power within him, and to cultivate a listening ear for what she has to teach him. In her honored position, she can help navigate him through life into higher spiritual planes, as in her highest manifestation, she is the "incarnation of meaning" itself.
As I write this, I wonder about how this relates to the Enneagram, because there is no gender with the Enneagram, but there is a direction in the flow towards destruction of self and others; versus towards healing and wholeness, depending on which way you're cycling through the triangle or hexad. This is all very fascinating. My guess is that a man or woman stuck in the forward motion of the cycle will manifest the unhealthy anima or animus, ie. they're trapped in their particular intelligence centre. But when a man or woman gets the impetus to make some major life changes, they start moving backward through the symbol and start integrating the shadow for a healthier, lighter, actualized Self.