Positively, the traditional teaching emphasizes that God is an inherently social being. Human unity approaches conformity to the image of God's unity through self-giving, empathy, adoration for one another, etc.. Such love is a fitting ethical likeness to God - but is in stark contrast to God's unity of being.
Three persons 
As in almost all orthodox versions of the trinity, the term 'person' is used to identify what the 'three' is. Social trinity argues that the three persons are each distinct persons, e.g. by suggesting that they have distinct centers of consciousness.
Many proponents of Social Trinity criticise modern individualism, suggesting that individual is not over against other persons. On the contrary, say these proponents, a person's identity and self are deeply constituted by their relationships, such that a person could not be the same person were it not for the relationship - the relationship, in some sense at least, precedes the person rather than the person preceding the relationship.
Two theological keys to the idea of person found in the social trinity are the trinitarian concept of perichoresis (associated most strongly with Saint John of Damascus), and the Christological doctrine of two wills in one person (which was central to Maximus the Confessor's defense of orthodoxy).
One being 
As in almost all orthodox versions of the doctrine of the trinity, the term 'being' is used to identify the 'one' in the trinity. Social trinity argues that this one being comes to exist as a result of a loving relationship between Father, Son, and Spirit. This relationship is in some respects like human relationships, but in many respects it promotes a greater unity. They often understand the idea of perichoresis of the persons of the trinity as providing at least part of this greater unity.
See also 
- Karen Kilby, Perichoresis and Projection: Problems with the Social Doctrine of the Trinity, First Published in New Blackfriars October 2000, URL accessed 12 January 2007.
- Theology for the Community of God, pg 76, Stanley J. Grenz, Wm. B. Eerdmans Publishing, 2000, ISBN 0-8028-4755-2: "At the heart of Christian understanding is the declaration that God is triune - Father Son and Spirit. This means that in his eternal essence the one God is a social reality, the social Trinity. Because God is the social Trinity, a plurality in unity"
- Against Eunomius, esp. 2.12, Gregory of Nyssa, at CCEL