The Trinity is an essential tenet of the Christian faith. The Trinity is also a tenet that is misunderstood by many and ridiculed by others. It might be called illogical. After all, this doctrine teaches that the one God is in three persons—Father, Son, and Holy Spirit. Some would, then, accuse Christianity of tri-theism, i.e. that we believe in three gods. Yet this is not what the Trinity is. True Christianity holds firmly to monotheism, that there is only one true God, and that that God is Yahweh of the OT. Yet, the doctrine of the Trinity teaches that Yahweh has revealed Himself in three distinct persons. Yahweh has revealed Himself as the Father, as the Son, and as the Holy Spirit; however, He is one God. Now I imagine that few would argue against the deity of the Father, but what about the Son and the Spirit.
For the sake of space, I will only make one point about the divinity of both the Son (Christ) and the Spirit. When you read the NT and see the title of Lord ascribed to Jesus Christ, and even to the Spirit, it means nothing less than that the Son and the Spirit are God, co-equal with the Father. This is even clearer when we go to the Greek of the NT. The word translated Lord in the English versions of the NT is Kurios. Kurios is also the word used in the Greek OT (Septuagint) for the Hebrew word translated LORD in English versions of the OT, YHWH (Yahweh). This connection is seen quite explicitly in Romans 10. In Romans 10:13, Paul quotes from Joel 2:32, where it says “And everyone who calls on the name of the LORD will be saved.” Now Paul quoted this verse from the Septuagint where the Hebrew YHWH is transmitted into the Greek as Kurios. What Paul teaches in this portion of Romans 10 is that anyone who confesses, “Jesus is Lord” will be saved. So he says, “For there is no difference between Jew and Gentile—the same Lord (Kurios/Yahweh) is Lord (Kurios/Yahweh) of all and richly blesses all who call on him, for, ‘Everyone who calls on the name of the Lord (Kurios/Yahweh) will be saved’” (Romans 10:12-13 parentheses added). So, when we confess Jesus as Lord, we are identifying Him as Yahweh. In 2 Corinthians when Paul says the Lord is the Spirit, he is saying the Spirit is Yahweh. Therefore, the Son is God and the Spirit is God.
There are some popular analogies drawn from the natural world to illustrate the Trinity. Some like to use the egg with the yoke, the white of the egg and the shell. I personally like water as an analogy with its three material phases—solid, liquid, gas. Whether it is solid ice, refreshing liquid, or in the vaporous gas form, water remains to be water. Now, like any analogy, this is hardly a perfect picture of the Trinity. It is best to understand that Yahweh, the one true God, has revealed Himself as Father, Son, and Spirit; moreover, it is important to understand that these three are distinct persons, i.e., the Father is distinct from the Son, and the Son distinct from the Spirit. Nonetheless, they are all Yahweh/Kurios. The only reason this seems illogical is that it is so difficult for our finite understanding to comprehend. This is why Scripture is so important. God is so beyond our understanding. So, we need Him to tell us about Himself, and we need His special revelation so that when someone claims to have a revelation about God, we can measure against what God has revealed about Himself in Scripture; and it is important to understand that Scripture is not a man-made revelation as it is often alleged today. The OT and NT Scriptures are a consistent revelation of God and His redemptive purpose in Jesus Christ written by various authors over many centuries (about 4,000 years in fact). The Scriptures reveal to us the nature and character of God, and this nature and character of God is consistent throughout the 66 books of the Bible. The Trinity is no less part of that revelation, which is why it is considered an essential doctrine of Christianity.