This does not mean that we do not relate to others. It means that we have to know who we are and not just what the important people in our lives expect us to be. Some of us are so caught up with doing things that we don't have a chance to experience who we are or just being. Existentialists believe that we can derive strength from the experience of looking to ourselves. We can give our lives meaning and decide how we will live.
Relationships then become life affirming.
Because we are able to stand alone and are not dependent we can establish relationships based on fulfillment not depravation. No matter how closely we relate to another individual, there remains a final unbridgeable gap. There is a conflict between the awareness of our fundamental isolation and the wish to be protected, to merge and to be apart of a larger whole. All humans search for a sense of significance and purpose in life. We all can have an internally derived value system that does provide a meaningful life.