I had a dream about someone and that person had a dream about me that same night.
If you know this person, or very close to him/her or have the same experience in reality, that may happen. Projecting dreaming of each other could reflect the need of sharing at night time. In other words, you both may not get enough in day time. Dreaming of each others at night time is a reflection of how much you care for each others.
However, if you don’t know him/her at all, then it could just be coincidence, and this coincidence can be related to what you both experienced in life time.
For example, this person you are not that close goes to a theater and you go to the same theater watching same movie (but sit different seat), both of you glanced at each others. That may glance may lurk into your subconscious mind and easily become dream.
It may be mere coincidence. The mind, including the subconscious is not tangible and yet not abstract. It is real but not confined by the physical world. Were you communicating? What happened in the dreams? Were you both subconsciously expressing you feelings about each other or “to” each other?