The Holy Trinity is a mystery that will always remain a mystery to us on earth. I suspect it may even remain a mystery when we are in heaven--that is, we will always marvel at it but never grasp it. But this truine nature is how God reveals himself to us. He tells us who he is. He does not ask us to understand it. He does not submit it for our approval. God is one; God is three -- trinity in unity and unity in trinity. Don't get it? Don't feel bad. No one does. But it is precisely how God reveals himself to us.
We worship one God (Deuteronomy 6:4); we worship three persons within that one God -- Father, Son, and Holy Spirit (Matthew 28:19). We believe in one God (Nicene Creed); we believe he is Father, Son, and Holy Spirit (3 articles of Nicene Creed).
Whether you have already seen it or not, check out the Lutheran Satire video below. St. Patrick, Donall, and Conall help to explain why analogies to grasp the Trinity just do not work. Brilliant! Enjoy!