One of the common images used to help us understand the concept of the Trinity is that of an egg which has three parts (shell, yoke, and white) but is still just 'one' egg. Other images often used to help clarify this abstract concept are the three properties of water (ice, water, vapour) or a three-leaf clover. These are helpful in a limited way but they fail to communicate fully the intimacy within the Godhead(and why the concept of the Trinity matters).
Our minds find it easy to differentiate the three roles of God as revealed in Scripture: the Father as Creator and Sustainer, the Son as Redeemer (Saviour), and the Holy Spirit as Sanctifier (one who is working holiness in us and calling us back to Jesus). More difficult is to put those three distinct roles together so that they are not three completely separate beings but three parts of one.
Whenever one part of the Trinity talks about another, there is always a closeness assumed; read John 14:15-30 to see what I mean. It is this closeness that makes the Trinity an important part of our everyday life with God because we are not distant from God but have the Holy Spirit in us. That means God in His fullness is dwelling with us, knows us, and cares for us every step of our journey; we have the Holy Spirit who leads us into the truth, forgiveness, and life of Christ who in turn has made it possible to share life forever (as originally intended) with our loving and creative Father. Our whole life holds together in the relationship of God the Father, Son, and Holy Spirit.
This was so important to the early church that they spent years defending the concept of the Trinity as a unity of three persons. The Athanasian Creed was developed to safeguard the truths about God which were increasingly coming under attack. Once a year, on Trinity Sunday, we read the Athanasian Creed (which admittedly is long and repetitive) as a means of reorienting ourselves amid a disorienting and fragmenting world that would lead us astray from God as revealed in the Scriptures.
Here is the text of the creed (click the link). It has strong language about the necessity to confess these teachings which reminds us in a shocking way of what is at stake. I challenge you (and it will be a challenge) to read through the creed trying to understand what’s being communicated and use it to sift your understanding of God.
May you be blessed as you are reminded of God the Father, Son, and Holy Spirit’s continued work and presence in your life!