Answering the often raised objection to Trinitarianism:

I have had many conversations with Trinitarians and all of them that I have had conversations with will say this:

The Father is God (that's 1 God)
The Son is God (that's 1 God)
The Holy Spirit is God (that's 1 God)

If you add them up, that's THREE GODS. Sorry, you can't get around that. 1 + 1 + 1 = 3
God is one What (essence) and three Who's (subsistences, aka Persons).

Essence and Person are not the same things. Essence refers to the being of God, while Person is used here as substance within being (subsisting as, subsistence).

The term Person does not mean a distinction in essence but a different subsistence in the Godhead. A subsistence in the Godhead is a real difference but not an essential difference in the sense of a difference in being. Each Person of the Godhead subsists or exists "under" the pure essence of deity. Subsistence is a difference within the scope of being, not a separate being or essence. All persons in the Godhead have all the attributes of deity.

Formally speaking, subsistence is the means of individuation of essence with respect to existence. Less formally, subsistence is the means by which essence exercises existence, or even more succinctly, subsistence means something that really exists.

So we can say that Person, with reference to the Trinity, means the one divine essence in a specific manner of existence and distinguished by this specific manner of existence from that one divine essence and the other Persons.

The divine essence does not exist independently along with the three Persons. The divine essence has no existence outside of and apart from the three Persons. For if the divine essence did, there would be no true unity, but a division that would lead into tetratheism.

Hence, Within the one Being that is God, there exists eternally three coequal and co-eternal persons, namely, the Father, the Son, and the Holy Spirit.

If we look a bit deeper the statement above can be parsed as follows:

1. There is in the divine Being (God) but one indivisible essence (ousia, essential, being), see Deuteronomy 6:4, 1 Corinthians 8:4, Galatians 3:20, 1 Timothy 2:5.
2. The nature of the one divine being, God, is inclusive of all the attributes of His being, that is, God is His attributes.
3. In this one divine Being (God) there are three personal distinctions (what the church throughout history calls Persons), or individual subsistences (personal modes of existence) Father, Son and Holy Spirit, see Genesis 1:1, 26, 3:22, 11:7, Isaiah 6:8, 48:16, 61:1, Matthew 3:16-17, 28:19, 2 Corinthians 13:14.
4. The whole undivided essence of God belongs equally to each of the three persons, see John 6:27, Romans 1:7, 1 Peter 1:2, John 1:1, 14, Romans 9:5, Colossians 2:9, Hebrews 1:8, 1 John 5:20, Acts 5:3-4, 1 Corinthians 3:16.
5. The subsistence and operation of the three persons in the divine Being is marked by a certain definite order, see Luke 22:42, John 5:36, John 20:21, 1 John 4:14, John 14:16, 14:26, 15:26, 16:7, John 16:13-14.
6. There are certain personal attributes by which the three persons are distinguished, see 1 Corinthians 8:6, Revelation 4:11, Revelation 1:1, John 3:16-17, 1 Corinthians 8:6, John 1:3, Colossians 1:16-17, John 1:1, 16:12-15, Matthew 11:27, Revelation 1:1, 2 Corinthians 5:19, Matthew 1:21, John 4:42, Genesis 1:2, Job 26:13, Psalm 104:30, John 16:12-15, Ephesians 3:5, 2 Peter 1:21, John 3:6, Titus 3:5, 1 Peter 1:2, Isaiah 61:1, Acts 10:38.