The Trinity though, is generally a combining of two core metaphysical concepts, being:
Godhead, and Logos.
The thing is that it is considered in varying degrees depending on the denomination to the semantics of the Triune Godhead. The Trinity itself, to some Christian traditions, offers itself as one of the spiritual
mysteries.
I do find the subject very interesting. The Logos aspect of Jesus leads some Christian traditions to differ in position between Jesus being a Divine representation and being God-incarnate.
From the strains of Gnostic and post-Kabbalistic influence, alongside many post 10th century Christian Mystics, there is the tendency to devalue Jesus in the category of just being a symbol of spiritual attainment....which obviously discounts a Trinity in that interpretation.
One of the areas of significance for the Trinity theology, is the pre-eternal existence (according to certain chapters in the NT) of Jesus applied back to Genesis 1, it's fascinating.
The Trinity as most commonly understood (to really answer the question) is that:
There are 'three persons in one', Father (YHWH), Son (Jesus) and Holy Spirit. They are all (in Trinitarian Christian theology) one God, not three. Jesus is the redeemer of humanity, he (God incarnate) sacrificed himself to wash away the sins of the world, for those that believe in him. He essentially broke the Ouroboros that started in the Garden of Eden. God sacrificing a part of himself is seen as the greatest act of love there could be.
(as to why there is still sin, is another thing that I have in my own speculative theological ideas....however, I'm not a Christian, so I'm not saying I believe in the Trinity personally....Jesus is one of our most beloved Prophets though in my religion)