If you dreamed of meeting your parallel self, this means that you are coming into contact with some aspect of your psyche or unconscious. You are recognizing a part of yourself that was previously repressed or undeveloped.
If you dream of searching for your parallel self but never finding her/him, you could be feeling insecure about the path you are taking in life, or trying to adjust to a new situation in which the rules and conditions are ever changing.
If it’s somebody else who you’re searching for without success, you have unresolved feelings about that person.