It's not that complicated, but it is a bit new to the human mind, it is transcendent. God is a Trinity because God is Love. As such, God cannot be just one eternal person, that would mean that interpersonal love has not been eternal. God can't be only two persons either; in such a case, love would be eternal, but it would not have a witness who also shares into this love. So, then, God must be three persons if He is to be love, the love between a Father and a Son witnessed by The Holy Spirit. All three Persons are equal because God is Love and so He is also humble. God can't be more than three persons either, that would make Him too relative, but He can create various beings that He can then make as Himself by deification (theosis). Now, if we look at God in relation to creation, we see that also God needs to be three Persons -- A Father who wants us as His children, a Son who can be an eternal model of son, and a Spirit who can make this possible by deifying us and bringing us into the same type of communion that The Father has with The Son; and, with The Holy Spirit and everybody, of course, but the main idea is that we are to be like The Son is to The Father, through the Power of The Holy Spirit. We see that even creation is gravitating towards being more like God, but without God or the creation becoming relative -- The Father does not cease to be Father, The Son does not cease to be the only-begotten Son, The Spirit does not cease to be the one Who deifies creation, and creation does not cease to be who they are either. Another thing about The Trinity is that they are three complementary parts, but they remain One God; that is The Son is not exactly merely another just like the Father, The Son is the Logos (Word) and Icon, or Wisdom of The Father, that is The Father has no icon in and of Himself, and same with The Spirit, The Father does not have spirit in and of Himself. In a way, The Father "gives up" his Logos and Spirit through begetting The Son and proceeding His Spirit. He doesn't "give up" because He is love, so He begets and proceeds out of love. Anyway, the point is that The Father alone, even though He is the only Person in the universe who is without a cause, cannot be God only by Himself (God would not be love), and so The Father begets and proceeds. The Logos and The Spirit do belong to the Father, but The Father is not God by Himself, He is only "one third" of God, He is the Will of God, but not the Logos and the Spirit (the two other parts). Also, we tend to think that The Father is superior, but it's not at all like that -- it's true, The Son and The Spirit cannot exist without The Father being Their cause, but it's also true that The Father cannot be God by Himself (He would not be love). It would then be wrong of us to not worship the three Persons equally because they truly do deserve the same dignity.