The Holy Trinity, Thrice Holy God, Thrice Loving God, three in One, yet One. The mystery of the Trinity is perhaps the most difficult doctrine to fathom. In the Old Testament Isaiah reveals the Thrice Holy God 'Holy, holy, holy is the Lord of hosts; the whole earth is full of His glory' (Is 6:3). In the New Testament, St John reveals that the essence of "God is love" (1 Jn 4:7). Love is what God is in essence. Love is not solitary. If love was solitary it would be wasted love. Love is given (Father), love is received (Son), loved is returned (Holy Spirit). This is Trinitarian love. The love of the Trinity is so generous, God literally spills over with love, and out of an overflow of selfless generosity He created liturgical beings (angels and humans) in order that we might participate in His Trinitarian love. God first loved us. Some call this a 'foolish love of mankind' (that is a love that goes beyond understanding). Free will is our greatest gift given to us by God - we are on this earth, a training ground, an obstacle course that tests and grounds our love - it tests our generosity to love - the first commandment is our guide 'to love God with all of our heart, all of our love and all of our mind'. As the catechism reminds us God made us to know Him, love Him and serve Him in this world, and be happy with Him forever in the next.
Trying to understand the Trinity using human concepts is really difficult. God is One yet Three. The fire of God's love. Fire has a three-fold character - yet is one. Fire (God the Father), Light (God the Son), and Heat (the Holy Spirit).