The doctrine of the Trinity is the theological/philosophical apparatus necessary to talk sensibly about and hold together an apparent paradox as truth:

1. “Hear, O Israel: YHWH is our God, YHWH is One” (Deut. 6:4). The foundational theological confession about the identity and nature of God in Israel’s Scriptures — the confession on which the theological unity of those Scriptures depend — is that there is one God, the sole subject of worship, the sole Creator of heaven and earth and all that is in them, incomparable with any other putative god, incommensurable with any creaturely reality.
2. “Go and make disciples of all nations, baptizing them in the name of the Father and the Son and the Holy Spirit, and teaching them to obey all that I have commanded you” (Mt. 28:19f). The foundational theological confession about the identity and nature of God in the New Testament — the confession on which the theological unity of that Testament depends — is that the One God of Israel is to be rightly worshipped in the person of the Father of Jesus Christ; also worshipped in the person of Jesus Christ, the unique and eternal Son of the Father; and also worshipped in the Spirit of Jesus Christ, who is given freely by the Father to all those who belong to Jesus Christ.
3. And yet these three are not three gods, but one God.

In other words: the Church is right to worship Father, Son, and Holy Spirit as God alone, and in that worship they are (despite appearances!) in essential continuity with Israel’s worship of the One God YHWH. That is what the doctrine of the Trinity is seeking, in a theological register, to articulate.