The doctrine of the Trinity is the church’s best attempt to do justice to the whole Bible’s teaching on God. From the fact that Jesus is Lord – Jesus who himself is begotten of the Father who is Lord, Jesus who sends us the Holy Spirit who is also the Lord – plus the fact that by definition there can be only one Lord to whom every knee should bow, the church thereby proclaims that there are three persons in one God: each person fully and truly God, yet there are not three Gods but one. Moreover, the doctrine of the Trinity states that God is not one person only who however assumes 3 different roles (e.g., the one and the same person can be a father to his son, a son to his own father, and a husband to his wife) but three persons: the Father is not the Son or the Spirit; the Son is not the Father or the Spirit, and the Spirit is not the Father or the Son. God therefore is plurality in unity, and unity in plurality: all three being one in essence and equal in dignity and power. In order to make this clear the church has even dared to use an extra-biblical term (i.e., trinity) in order to safeguard a biblical truth.
What happens, then, if we deny the doctrine of the Trinity? What is at stake? Here is Karl Barth’s answer:
“… all anti-trinitarianism is forced into the dilemma of denying either the revelation of God or the unity of God. To the degree that it maintains the unity of God it has to call revelation in question as the act of the real presence of the real God. The unity of God in which there are no distinct persons makes it impossible for it to take revelation seriously as God’s authentic presence when it is so manifestly different from the invisible God who is Spirit. On the other hand… to the degree that it is ready to maintain revelation but without acknowledging the substantial equality of the Son and the Spirit with the Father in heaven, the unity of God is called in question. In its concept of revelation it will not in fact be able to avoid interposing between God and man a third thing which is not God, a hypostasis which is not divine – it does not want that – but semi-divine; it cannot avoid making this the object of faith. In so far as it is not a denial of revelation, antitrinitarianism in any form is a cruder or subtler deifying of revelation.” (Church Dogmatics, I.1, T&T Clark International, 2004; p. 352)
Barth goes on to say, “If Christ is not very God, what else can faith in Him be but superstition?”
This is a very important point. The Bible rejects tritheism (this is to be distinguished from trinitarianism): there is only one God, the only one who is good and who is worthy of worship. But the Bible teaches us that Christ is to be worshipped. It is not enough to answer that he is to be worshipped because God so commands. The reason for the command must be sought out. And as for the Holy Spirit: “the Lord is the Spirit” (II Corinthians 3: 17-18). When Ananias and Sapphira lied to the Holy Spirit Peter says they lied to God (Acts 5:3-4). Moreover, in Christ God was truly present with us (Matt. 1:23). He is the true and full revelation of the Father (see Heb. 1 below). In him God was reconciling the world to himself (II Corinthians 5:19). And all this can be said about Christ because Jesus Christ is the true God and everlasting life (I John 5:20).
From Hebrews chapter 1 (ESV):
1:1 Long ago, at many times and in many ways, God spoke to our fathers by the prophets, 2 but in these last days he has spoken to us by his Son, whom he appointed the heir of all things, through whom also he created the world. 3 He is the radiance of the glory of God and the exact imprint of his nature, and he upholds the universe by the word of his power. After making purification for sins, he sat down at the right hand of the Majesty on high, 4 having become as much superior to angels as the name he has inherited is more excellent than theirs.5 For to which of the angels did God ever say,
“You are my Son,
today I have begotten you”?
“I will be to him a father,
and he shall be to me a son”?
6 And again, when he brings the firstborn into the world, he says,
“Let all God’s angels worship him.”
7 Of the angels he says,
“He makes his angels winds,
and his ministers a flame of fire.”
8 But of the Son he says,
“Your throne, O God, is forever and ever,
the scepter of uprightness is the scepter of your kingdom.
9 You have loved righteousness and hated wickedness;
therefore God, your God, has anointed you
with the oil of gladness beyond your companions.”
“You, Lord, laid the foundation of the earth in the beginning,
and the heavens are the work of your hands;
11 they will perish, but you remain;
they will all wear out like a garment,
12 like a robe you will roll them up,
like a garment they will be changed. 
But you are the same,
and your years will have no end.”