Through Jesus, we see that divine persons are persons in relation. They are who and what they are in distinction from and yet in relation to one another within the one communal being of God. The Father is different from the Son and the Spirit.  And the other two persons are different from the Father and each other.  Each person is different and has distinct characteristics.  And yet the differences do not divide them as separate individuals.  In their differences, the three are interrelated with one another. 

Does that change the way we see ourselves as persons?  Should we no longer consider ourselves individuals apart from other persons?  I think so. Jesus shows us that persons are who they are in relation to other persons. That means we should not consider people as individuals who may form relationships.  We are who we are in relations. That means we are called to depart radically from all forms of individualism.  For example, we no longer see the church as a gathering of individuals who come together so that each individual can be blessed and depart to live his or her individualistic life more fruitfully.  The church is essentially a communion of persons in union with Jesus and in him sharing personal communion within the Triune Communion.  Father, Son and Spirit are who they are in in their communal life.  And they have opened up their communal life to include us. And in this communion with the Triune God, we share in his communal life as a Spirit-enabled and Spirit-led communion of persons.  We are definitely not a mere collection of individual believers who come together for the good of the individual.