God as Three in One
God transends our capacity to understand. It is like the way that our eyes, designed to look for food and danger and recognising others, struggle to take in the tiny things, like individual molecules of water, without a microscope. Equally our eyes cannot take in truly massive things, like the curvature of the horizon at sea, without a special camera. So too, our efforts to take in God require special tools, and even then the picture we get is full of mystery. So, the Trinity is a special tool we can use in an attempt to understand and talk about God.
Our belief in the Trinity is the belief in One God, who is a Triune God: One divinity in three persons. God the Father, God the Son, and God the Holy Spirit are all God, and are one God.
God as Love
God loves everyone and everything, but loving isn't just a thing that God does. Love is who God is; our God is love.
Love can't exist alone; it exists as a relationship between things, and so identifying God with love means identifying God as a relationship and the Trinity also helps us understand this.
The love between the Father and the Son and the spirit is eternal - before there was anything, God was love, and everything that exists, has existed, or will exist, is the outpouring of this super-abundant love.
People often think of God the Father, creator God, as the God of the Old Testament, but really all three persons of the Trinity are at work throughout the whole story. Jesus wasn't 'created' or split off from God at the beginning of the New Testament. Rather Jesus, the divine Word of God, has existed forever and was the very Word that God spoke the world into being, and the same Word that God spoke to the prophets.
God as neither Man nor Woman
The names God the Father and God the Son use male concepts and, likewise, the Holy spirit is often referred to using the male pronoun 'He'. This can complicate our understanding of God. The Catechism of the Catholic Church states that, "God transcends the human distinction between the sexes. He is neither man nor woman: He is God". Any gendered language used about God does not and cannot limit God.