When I was a young child, the Trinity was explained to me using an egg. It was one egg yet consisted of the yolk, white, and shell. That was enough to satisfy the theology of a six-year-old boy.
Later I read about the legend of St Patrick using the shamrock to explain the concept of the Trinity to one of his congregation and how the three leaves were connected together on the one stalk.
While that helps some, I still struggled with understanding the Trinity. I like having answers to questions but this one continued to elude me. Early in my walk with Christ, as I continued to try to gain an understanding of the Trinity, I had learned that Alexander Hamilton used Isaiah 33:22 in the design and construction of the foundation of our federal government:
"For the Lord is our judge; the Lord is our lawgiver; the Lord is our King; he will save us."
In that verse I not only saw the three branches of government (judicial, legislative, and executive), but I also saw the Trinity (God the Holy Spirit, God the Father, and God the Son) represented. Each branch represents the government as a whole, yet each has its own specific function; and so it is with the Trinity.
In the Trinity, the Holy Spirit is the one who convicts us of our sin (John 16:8), God the Father gave the law to Moses (Exodus 20:1-17), and God the Son is the King of kings who will reign forever (1 Timothy 6:14-16). Though separate in function, they are one as God.
However, there are some very important contrasts that must be made here.
In government, we can choose our leaders. God is God regardless of whether or not we recognize him as God.
All governments are filled with flawed and broken people. God is pure, flawless, perfect, and holy. He is incorruptible.
The roles mentioned above for each member of the Trinity, or Godhead, cannot fully define the scope of an infinitely awesome God with infinite love and infinite mercy (Job 5:8-9).
Finally, as I focused on memorizing the book of Titus while I spent time in a State Sponsored Spiritual Retreat (aka CTF in Soledad, CA) I came across a passage in the third chapter of Titus that beautifully illustrated how the full Trinity is at work in our salvation.
But when the goodness and loving kindness of God our Savior [the Father] appeared, he saved us, not because of works done by us in righteousness, but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit, whom he poured out on us richly through Jesus Christ our Savior, Titus 3:4-6
What I see in that passage above was that if God is our Savior and Jesus Christ is our Savior (also see Titus 1:3-4) and the power to be regenerated (born again) is through the Holy Spirit, then they must be connected in purpose and person. Now while the belief and acceptance of the Trinity is not necessary for salvation, it is an important doctrine of the church and is a worthwhile pursuit to learn more about. Salvation is through belief and surrender to the person and work of Jesus Christ alone.
The author of Titus, Apostle Paul, follows those three verses with this conclusion.
So that being justified by his grace we might become heirs according to the hope of eternal life. The saying is trustworthy, and I want you to insist on these things, so that those who have believed in God may be careful to devote themselves to good works. These things are excellent and profitable for people. Titus 3:7-8
It is so wonderful to know God and to know him more and in deeper ways through his Word, prayer, and fellowship with others who are in active pursuit of the joy and happiness that only he provides.