What it usually means
Start with the man himself. A dream about your father may be about him directly: a conversation that never happened, a worry about his health, an old disagreement, a recent phone call, his ageing or his death. If he has died, dreams of him are a normal part of grief and are often a way of continuing the relationship.
Beyond the literal, the father in a dream frequently stands for a set of qualities rather than a person: authority, rules, protection, judgment, the world outside the home, and the question of whether you are doing well enough. Many people carry an inner version of their father's voice long after they have left his house, and the dream may be about that voice rather than the man.
His mood in the dream is a strong clue. Pride and approval often appear when you are seeking confirmation that a choice was right. Anger or disappointment often appear when you are judging yourself harshly. Absence often appears when you are facing something without the guidance you wanted.
If your relationship with your father was painful or he was not there, these dreams can be difficult. They may circle around what was missing rather than what happened. That deserves care rather than interpretation, and if the dreams are distressing it can help to talk them through with someone you trust.
What changes the meaning
A proud or approving father. A wish for recognition, or a sense that you have earned it.
An angry or disappointed father. Self-criticism, or fear of failing a standard you absorbed long ago.
Arguing with your father. Asserting your own direction against an old authority; sometimes an unfinished conflict.
Your father ill or ageing. Concern for him if he is getting older; otherwise a sense that a support or certainty is weakening.
Your father dying. Rarely a prediction. More often the end of a stage in the relationship, or your own move into a role he once held.
A father who has died, alive again. Common in grief; often a reassurance, sometimes a sense of something unsaid.
Being your father. Noticing his habits or decisions in yourself, or stepping into his kind of responsibility.
Your father as a child. Seeing him as a person with his own history and limits, rather than as an authority.
Searching for your father. Looking for guidance, protection or permission you feel you lack.
Someone else in your father's place. A boss, a teacher, a partner or a mentor who plays that role now.
When it keeps coming back
Recurring father dreams often follow major changes in the relationship: his illness or retirement, your own parenthood, a move, a reconciliation or a break. They usually settle once the change has been absorbed.
If they return without any such change, look at where you are dealing with authority in waking life. People often dream of their fathers during conflicts with bosses, institutions or rules, and when they are making decisions they expect to be judged for.
Becoming a parent or a leader yourself is another common trigger. The dream may be rehearsing what kind of authority you want to be.
In Jungian terms
Jung's own father was a country pastor who, as Jung saw it, had lost his living faith but kept performing its duties. In his memoir Jung describes the pain of watching this and of being unable to talk to his father about it. Much of his later thinking about religion and authority grew from that relationship.
He also wrote about the father as an archetype: an image of order, law and spirit that lives in the psyche independently of any real father, and that the personal father is never quite large enough to fill. Part of growing up, in his view, is separating the two — seeing your father as a man, and finding the authority he represented within yourself.
A father dream can therefore be read in two directions at once. It shows how you stand with him, and it shows how much of his authority you have taken over as your own.