The Trinity is a very complicated topic. Its design is impossible for the mind to comprehend, but I will attempt to explain. From what I understand, the doctrine of the Trinity is that there are three biblical affirmations of the Trinity.
The first affirmation is that God is three persons: the Father, the Son, and the Holy Spirit. The Son is not the Father, The Father is not the Holy Spirit, and the Holy Spirit is not the Son; they are all separate persons.
The second affirmation is that each one of these persons is God. The Father is fully God, the Son is fully God, and the Holy Spirit is fully God.
The third affirmation is that there is only one God. Even though the Father, the Son, and the Holy Spirit are all God, they are not three Gods, because God is one being.
Now how can I understand this? This sounds as if it is a contradictory statement, however, it is not. It is simply understanding that this concept is beyond human intelligence. My mind is not capable of comprehending such a system. We cannot picture such a system because our minds can only picture things from the world around us. In fact, we will never be able to fully understand the Trinity.
Someone may come up to me and ask, “How can you believe in a concept you do not know or understand?” I will respond, “I believe in God. I don’t fully know or understand him; in fact, nobody does. But is that not a part of faith as well?” I do not understand the Trinity, but I believe in it. In the same way, I do not understand God, but I believe in Him.