Perichoresis is a Greek term used to describe the triune relationship between each person of the Godhead. It can be defined as co-indwelling, co-inhering, and mutual interpenetration. Alister McGrath writes that it "allows the individuality of the persons to be maintained, while insisting that each person shares in the life of the other two. An image often used to express this idea is that of a 'community of being,' in which each person, while maintaining its distinctive identity, penetrates the others and is penetrated by them." 
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Perichoresis in application
The New Testament demonstrates that God brings glory to himself. John's Gospel is important in understanding how Jesus and the Father relate; a key passage for a perichoretic understanding of God's glory is John 17:1, where Jesus prays, "Father, the hour has come; glorify your Son that the Son may glorify you." We see that the Son brings glory to the Father, the Father brings glory to the Son, and the Spirit brings glory to the Son (cf. John 16:14). Such an understanding of glory exhibits the love expressed within the Godhead by Father, Son and Spirit as they give glory to each other.
- Christian Theology, p. 325.
- Alister McGrath, Christian Theology: An Introduction, 3rd ed. Blackwell, 2001.