Lucy Burroughs answered
Some people believe that meaning and significance can be assigned to the things we dream about. This is called dream interpretation, and consists of giving symbolic significance to the content of our dreams. Like horoscopes and palm reading, this has not been proven; however, it is possible that there is some kind of psychological or subconscious significance to dreaming.
Dreams of Being Chased
Dreams of being chased are often taken to mean that the dreamer is avoiding a problem in their life. The distance between you and the person chasing you can be said to signify the distance between you and the thing that you're avoiding. This could be an uncomfortable situation that you don't know how to deal with, like breaking up with a long-term partner.
Dreams of a Cliff Edge
If you dream that you're standing on the edge of a cliff, this could be interpreted to mean that you have reached a new level of understanding in your life. Alternatively, it could mean that you are facing a life-changing decision. Given that you also dreamed that you were being chased, it's more likely to be the latter; you've been avoiding a difficult situation, and now you have to face it, and make a decision.