To dream that you are engaged to be married represents sexual or relationship needs. You may be trying to resolve your feelings of loneliness. Alternatively, it symbolises your commitments and desires for security. More directly, if you are unmarried, the dream may indicate your desires for some form of commitment.
If you dream that you are engaged to your father, then it implies that you are looking for a father figure. The dream does not mean that you want to actually marry your father. Perhaps your father is not around much and you just want more of a relationship with him. Alternatively, the dream may mean that you want someone who is as good to you as your father.
To dream that you break an engagement denotes a hasty and unwise decision in some important matter.
To dream of a business engagement signifies concern and worries in some area of your work.