Even after you have removed this person/people from your life the cord still exists between you and follows you into your next relationship. The cord that is with you from that past relationship moves with you and can still effect you both in many ways. Maybe you can't stop thinking about them, even though you want to forget so much it just never goes away, or not as quickly as you would like.
Cord-cutting is a process that negative energetic attachment between you and another person/people so that the patterns of that past relationship do not affect your behavior in the present or your ability to have a healthy strong relationship without issues that may not be a reality in this new energetic cord. This means that the anger, feelings of inadequacy, poor self worth, people pleasing, that were formed and caused patterns to emerge can be eliminated.