This has a great many levels of meaning. Basically it is a looking at yourself, a self examination; and the face in the mirror may not match your own. It may be better or worse. That is, in self examination you may come across, or see, parts of our nature that are the worst side or the best side of yourself. These re the things you do not usually see about yourself. You may, for instance, see innate possibilities as they would be in full bloom. But the mirror might only reflect your negative worries about yourself, or how you think you appear to others. Worries about ageing might be one of these. Nevertheless, the dream process usually tries to lead through worry to growth.
The mirror appears in many religious symbols and in much folklore. Water was probably the first mirror, and as such represents human consciousness, soul, or self awareness. This looking at oneself can therefore be a way of depicting self awareness, your ‘I’, as a distinct individual.
Alice goes through the mirror to enter Wonderland, which is again symbolical of looking within self, and exploring unconscious contents.
Indian and Buddhist philosophy use it in a slightly different way, as also Yoga teachings. It is explained that when we look at a mirror we do not see its actual surface. We do not see the actual mirror, only the images reflected on its surface, which appear as reality. Likewise, mind or consciousness is like a mirror. In it we see the images of physical existence and life experience, which we take to be the only reality. But the Yogi asks himself, what is this that is conscious of all these images? What is this mirror we call consciousness? Who am I?