The doctrine of the Holy Trinity is one of the essential mysteries of the Christian faith. By 'mystery' we mean the lofty knowledge God has condescended to reveal to us in Scripture. However, 'mystery' does not imply that this knowledge is nonsensical or irrational or inscrutable.
The rationale for saying that God is both One and Many may be clarified by means of an analogy to the One and Many problem in the history of philosophy.
"Is the world one thing or many things?" This question was first studied by the ancient Greek natural philosophers. Some, such as Thales and the Eleatics, said the world was one thing or substance (water, air or some other element). This would account for the continuity of the world, but it doesn't account for its appearances of diversity and change.
Others, such as Democritus, said that the world was made of a numerous or infinite number of things, or (as Heraclitus said) a constant flux of change and diversity. This accounted for the changing appearances and variety in the world, but left no place for continuity or stability. Furthermore, neither of these views gave any impetus to the study of nature. If nature is one, then everything is fundamentally the same Being, and there is no point in studying illusory appearances. If it is many, then Being will not be knowable or namable; we are left in a speechless flux.
Aristotle in the Physics proposed the resolution of this quandary in terms of a composite (synalon) which placed both unity and diversity as equally ultimate and inherent in nature. The world is both one thing and many things. This is not a contradiction provided the world is one in one sense, and many in another sense. The One is the substrate, the common ground. The Many are the varieties of things or changes of appearances. Both terms are equally important to give a rational account of the world.
This composite principle of the One and the Many resolved the debate, and also provided a firm foundation for the rational investigation of nature in the West. Without this resolution, knowledge of nature collapses into either monism on the one hand, or a Heraclitean flux on the other.
In the history of the Church, a similar controversy arose as to the status of the Son and Holy Spirit. If they are divine, then is Christianity teaching three Gods? If God is one, then what do we make of the many verses of Scripture that imply that the Son and Holy Spirit are also divine?
This debate was resolved by the Council at Nicaea in AD 325. The Nicene creed states "We believe in one God the Father Almighty, ... and in one Lord Jesus Christ, ... Very God of Very God, begotten, not made, being of one substance with the Father... and we believe in the Holy Spirit, the Lord and Giver of Life, who proceeds from the Father and the Son....
John Calvin's confession of 1566 is more technical: "Thus there are not three gods, but three persons, consubstantial, coeternal, and coequal; distinct with respect to hypostates, and with respect to order, the one preceding the other yet without any inequality. For according to the nature or essence they are so jointed together that they are one God, and the divine nature is common to the Father, Son, and Holy Spirit."
There is a clear parallel in the language, logical structure and history of the One and Many principle and the Trinity. This principle successfully opened the way to a rational understanding of nature, and a harmony of the statements of Scripture. A skeptic may say that the Trinity doctrine was therefore simply borrowed from the Greek philosophers before Christ. But that puts the cart before the horse. God is also the Creator of the natural world. If the unity/diversity structure is intrinsic to the character of God, then it is not a coincidence that this is also the way God created the world. It is therefore no wonder that philosophers encountered the problem of the One and Many as soon as they began to consider nature seriously.
The Trinity doctrine is what makes Christian theology Christian. Without it, theology moves toward either monism or polytheism without adequate defense.