The Christian teaching of the trinity says that the eternal God has among His traits the characteristic of “One-ness.”
This is a vital teaching for Christians since we are not polytheists. There is only One God. This teaching an be found clearly in the Jewish roots of Christianity – arguably the oldest of the Monotheistic faiths. Perhaps the core teaching of Israel is this: “Hear, O Israel: The Lord our God, the Lord is one.”
Christianity is not a return to polytheism. Christianity is committed to the truth that there is only one God.
However, as the person of Jesus Christ came and then, after Him, the Holy Spirit came into the picture as well, the theology of what it meant that God is One became a conversation again.
The problem was that Jesus said things like:
“Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, 20 teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.”  Matt 28:19
And the entire conversation in John 15, which began to beg the question early on as to the nature of Christ and soon thereafter, the nature of the Holy Spirit.
Paul wrote freely (I Thess 1:4-7, Phil 3:3, Col 1:16 and others) clearly linking God the Father and the Son and the Holy Spirit. Peter, who traveled with Jesus, opened his letter to the scattered Christians with :
“To those who are elect exiles of the Dispersion in Pontus, Galatia, Cappadocia, Asia, and Bithynia, 2 according to the foreknowledge of God the Father, in the sanctification of the Spirit, for obedience to Jesus Christ and for sprinkling with his blood:”
Of course, John’s theological gospel opens with passages directly stating that “The Word was God” and then making the connection clear that Jesus was that Word (John 1:1-14).
These teachings and many others caused the early theologians among the Christians to begin to wonder at the nature – the essence – of Jesus Christ and the Holy Spirit. How could they be God and yet Yahweh be God? How could they be distinct in their existence and yet still one?
Many of these people were trained as philosophers and were early Christian theologians. It is important to not see them as unsophisticated in their understanding of the nature of knowledge and truth.
In fact, most of them could probably have trounced most of us in a philosophical debate. Many were dedicated to the idea of the nature of God being rational – not incoherent or full of logical impossibilities.
At the basic level, the idea of three-ness and one-ness are NOT logical failures…
Anyone might has a dozen example of things that are three and are also one. Over the years, many of these have become famous exactly in the efforts to teach about the Trinity… and though seriously flawed for that task, they do show that something can be three and yet still be one.
Consider many substances. Many, like water, can be in gaseous, liquid or solid states and yet they are still the same substance at the molecular level.
Or, how about an egg being made up of various part… shell, albumen, yolk? One egg made of three different parts.
Or, consider that one person can be a sister, a mother, and a daughter, for example… and yet they are still one person.
Please note that NONE of these are correctly or directly analogous to the way that God is three and one. As a unique being, it would be expected that His particular existence is also unique.
However, it is significant that “three-ness” and “one-ness” can reasonably be traits of the same entity.
So, is it rational that God could be three and still also be one? Yes.
I am not making the claim that this proves that He is, of course… just that it is not irrational to believe it.
 The Holy Bible: English Standard Version. (2001). (Dt 6:4). Wheaton: Standard Bible Society.
 The Holy Bible: English Standard Version. (2001). (Mt 28:19–20). Wheaton: Standard Bible Society.
 The Holy Bible: English Standard Version. (2001). (1 Pe 1:1–2). Wheaton: Standard Bible Society.