Every time we have and emotional association with someone, we create a point of attachment to them, from our energy field to theirs.  Through this attachment, we maintain an energy exchange with them, regardless of time or distance, and regardless of your knowledge of it or our desire to maintain it.  You can imagine that after a certain time, these attachments (or cords) may no longer be a beneficial for us. The other person will continue to have some of your energy, and you will have some of theirs, and without even realizing it is happening, you may be influencing each other, often in negative ways.  These cords can create blockages in the flow of energy when they are created subconsciously, out of fear, or through the continual thought of a person one wishes to remain connected to.  Negative cords often form after an intense, long term relationship has ended. These cords can effect ones emotions and behavior, and in some cases create physical problems such as aches, pains and exhaustion. 
Regardless of how or why they are formed, negative cords of attachment can effect a person's energy, cause dysfunctional relationships, and subtle unsettled feelings, as we are effected by someone else's energy and intentions. 

Cord cutting helps:
Reclaim our personal energy
Grief after losing a loved one
After a painful ending of a relationship
Release toxic energy connections to people from your past, or current life