The phrase of "as of self" in Swedenborgian theology refers to the idea that though we as human beings are recipients of life from the Divine, our life must seem to us to be our very own so that we can have freedom and use reason in order to live as of ourselves. The freedom and reason we have isn't fully implanted in us, but it is continually joined to us. In power, origin, and inspiration it is Divine, but it is human in use. We exercise this ability when we act in all areas of life entirely as of ourselves, yet at the same time we should acknowledge that our life, as well as any truth we apply or good that results, is from the Lord.
The Lord gives us this "as of self" ability, so that we may have freedom, and thus have the chance to freely return His love. It keeps us from being robots, or slaves. We can receive and use the Lord's power, feeling that it is ours - making it real. At the same time, we can - in fact we need to - acknowedge that it isn't actually coming from us. This acknowledgment is critical; without it, a person will forget the idea of God, and depend only on self, which leads to pride, arrogance, and, eventually, hell.
The "as of self" doctrine is important. It shows how people can be spiritually free, and responsible for their regeneration, even though they can’t do any good from themselves.
(References: A Brief Explanation of the Teachings of the New Church 69; Apocalypse Revealed 224; Arcana Coelestia 1712 , ; Conjugial Love 134, 135; Divine Love and Wisdom 115; Divine Providence 42, 79; The Doctrine of Life for the New Jerusalem 101)