This is an excellent question and I believe most do not fully understand this principle. In our world, the human level if you will, one person is one being; thus, two persons are two separate beings. Now it is indeed interesting to consider why marriage in a sense is lifting up humans; primarily because it can sometimes have the effect of making two act as one. It introduces a 2nd dimension if you will; after all Christian marriage means two are to become one.
On the divine level one will still find personalities; however, they will be combined in extraordinary ways and because we have virtually no idea how it does work we can only speculate.
In God's dimension, if you will, you find a Being who is to us, 3 persons while remaining one Being. If you think of a cube you may perhaps "see" this better. Is not a cube made up of 6 squares yet remains one cube?
Father, Son and Holy Spirit, that is One (in three dimensions). I for along time was confused about this; I always assumed the father came first and then the Son came later followed or near the same time as the Holy Spirit. This is an incorrect assumption. If you engage in the Gospel of John, Christ said "I am" He was begotten not born. This makes sense to me now...
Here is what is of great significance, I will use an example, when a Christian prays he is trying to get into touch with God. Yet he should also realize that what is prompting im to pray is also God. You see it is God inside him. Yet he should reflect and realize that most all of his significant knowledge of God comes from Christ, the man who was God.
After my comatose experience, it was significantly clear to me that Christ was beside me every moment of my life. I had no idea, and felt like a complete idiot for both the things I had done and the things I had failed to do. I had my greatest Sacramental Confession after this.
Now, back to what I was saying before, you "see" when you are praying, Christ is right beside you, assisting with your prayer, praying for you. This is what is happening, first God is the "entity" which you are praying to or the goal you are trying to reach; God is also the entity or motive inside you pushing you on (this is why receiving Communion is so important, it is the Sacrament that helps put Christ in us); and God is (also) significantly the "bridge" which you are being pushed along to that goal. Therefore, this 3-fold life, Father, Son and Holy Spirit, the three dimensional representation of God is One yet in 3 manifestations or perhaps even more manifestations...