Dreams and Past Lives
In dreams we sometimes see things that we have never experienced in the present body. Sometimes in dreams we think that we are flying in the sky, although we have no experience of flying. This means that once in a previous life, either as a demigod or astronaut, we flew in the sky. The impression is there in the stockpile of the mind, and it suddenly expresses itself. It is like fermentation taking place in the depths of water, which sometimes manifests itself in bubbles on the water's surface. Sometimes we dream of coming to a place we have never known or experienced in this lifetime, but this is proof that in a past life we experienced this. The impression is kept within the mind and sometimes becomes manifest either in dream or in thought. The conclusion is that the mind is the storehouse of various thoughts and experiences undergone during our past lives. Thus there is a chain of continuation from one life to another, from previous lives to this life, and from this life to future lives.
Srimad-Bhagavatam (4.29.64) http://www.vedabase.net/sb/4/29/64
Prabhupada replied in a general way, saying that they are impressions stored within the mind, not just from this lifetime, but also from previous ones. The dream is illusory but the objects are real. Chuckling, he pointed to the plastic bottle of mustard oil I was using. "Here is a bottle of oil, and here is the bed. Both are real, but if I take the oil and put it under the pillow then it has no meaning. The pillow and oil are real, but I am crazy. That example is there in the Bhagavatam, of gold and a mountain. I have experience that there is gold, and there is mountain. I have no experience of a golden mountain, but in dream they combine."