Although the term “trinity” is not found in the Bible, the concept is clearly affirmed in multiple passages as an accurate understanding of the Godhead. While it may seem a headscratcher to believe in one God, in three divine persons (Father, Son and Holy Spirit), this is supported by the Scriptures.
The example that first comes to my mind is that of the baptism of Jesus:
Matthew: 3:13-17: Then Jesus arrived from Galilee at the Jordan coming to John, to be baptized by him. But John tried to prevent Him, saying, “I have need to be baptized by You, and do You come to me?” But Jesus answering said to him, “Permit it at this time; for in this way it is fitting for us to fulfill all righteousness.” Then he permitted Him. After being baptized, Jesus came up immediately from the water; and behold, the heavens were opened, and he saw the Spirit of God descending as a dove and lighting on Him, and behold, a voice out of the heavens said, “This is My beloved Son, in whom I am well-pleased.”
This passage illustrates all three at one time, ruling out the possibility that God simply manifested in different forms at different times. The Father did not come as Jesus, and then leave and return as the Spirit.
Got Questions addresses the objection that the trinity would mean tritheism, rather than being compatible with the monotheism the Bible obviously teaches:
“The Bible clearly affirms that there is but one God (Isaiah 43:10; 1 Corinthians 8:4). In addition, the Bible teaches the deity of the Father (John 6:27; Romans 1:7; 1 Peter 1:2), the Son (John 1:1-3; Hebrews 1:2; Titus 2:13; Colossians 1:16-17), and the Holy Spirit (Acts 5:3-4; 1 Corinthians 3:16). Moreover, the biblical writers go out of their way to affirm that all three Persons are distinct from each other (Matthew 28:19; Romans 15:30; 2 Corinthians 3:14). So, while it is true that the word trinity is not found in the Bible, the concept most certainly is.”
Matthew 28:19-20 is especially clear as Jesus tell his disciples: “Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the Son and the Holy Spirit, teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age.”
1 John Chapter 5 (especially verses 1-7) also refers to all three persons of the trinity: the Father, Jesus and the Spirit. There are certainly many other relevant passages such as Genesis 3 and 11 which include conversation between God the Father, the Son and Holy Spirit.
It may boggle our human brains, but that does not make trinitarianism any less true or biblical. I hope this is a helpful brief on the subject and if you are wrestling with the idea you will turn to the scriptures to settle the matter.
Resources for further study: