Dreams or visions in which you are packing tell you about an inner or outer journey, the start of a new life. Packing is the preparation for something new or an unexpected opportunity that presents itself. You may also be preparing to go on vacation, preparing to change, and so on in any form.
An alternative explanation is that you are closing a period of grief and you are letting go of that person. Pay close attention to what you are packing, what you put in the suitcase, what you wrap a piece of paper around it indicates what you are doing and what is important to you at the moment.