There is one divine essence, which is called and which is God, eternal, incorporeal, indivisible, of infinite power, wisdom, and goodness, the maker and preserver of all things, visible and invisible.
Yet there are three persons, of the same essence and power, who are also coeternal: the Father, the Son, and the Holy Spirit. And the term “person” is used, as the ancient Fathers employed it in this connection, to signify not a part of a quality in another but that which subsists of itself. (Article 1, The Augsburg Confession).
The concept of the Trinity is beyond human understanding. An illustration that might help us understand is the idea of dimensions. On a human level, one person is one being and two people are two separate beings. Just as one square is drawn on a piece of paper is one square and two squares are drawn on a piece of paper are two separate squares.
On the Devine level, you still find personalities but there you find them combined in new ways which we, who do not live on that level, cannot understand or imagine.
In God’s level, so to speak, you find a being who is three Persons while remaining one Being, just as a cube is six squares while remaining one cube. (This is only an illustration, we are not saying that God lives in another dimension.)