“The basic assertion of this doctrine is that the unity of the one God is complex. The three personal ‘subsistences’ (as they are called) are coequal and coeternal centers of self-awareness, each being ‘I’ in relation to two who are ‘you’ and each partaking of the full divine essence (the ‘stuff’ of deity, if we may dare to call it that) along with the other two. They are not three roles played by one person (that is modalism), nor are they three gods in a cluster (that is tritheism); the one God (‘he’) is also, and equally, ‘they,’ and ‘they’ are always together and always cooperating, with the Father initiating, the Son complying, and the Spirit executing the will of both, which is his will also. This is the truth about God that was revealed through the words and works of Jesus, and that undergirds the reality of salvation as the New Testament sets it forth.” (J.I. Packer)
For more on this subject, please visit the Systematic Theology page.