Before the Roman move to unify Christianity, many followers saw the trinity not as father, son and holy ghost, but father, mother and child. Some say they re-labeled the elements of the trinity to make the church more masculine. Maybe they did. It doesn't really matter what you label the elements though, the concept remains the same.
Calling it Father, Mother and Child may help us to understand what the trinity is. The father and the mother combine and form the child which unifies the three. If you want to remove gender from the equation, it could be creator, universe and life.
With this model, you can perhaps see why God made Eve from Adam's rib in Genesis. God made the Universe from himself to be his companion and together they made man, just as Eve came from Adam's body and together they made mankind.
It's a mathematical progression. One form begets another and the two beget a third. They are all separate, yet since they each came from the other, they are all one. The cycle becomes complete when you consider whether or not God and the Universe would exist as they are now if there were no sentient forms like humans to experience them.
The first unit splits. It becomes Father and Mother, or Father and Holy Ghost, or Ying and Yang, Order and Chaos, Life and Death, Light and Dark, Night and Day, Good and Evil, High and Low, Front and Back, Left and Right, creator and created, it is all the duplicities we know and more.
There are philosophies satisfied with just the duality, but there is a third step, the reunion of the two, creating a third. Consider the process of evolution from asexual to sexual reproduction. The first generation splits creating not identical copies but opposites. Here reproduction ends unless the opposites, male and female, come together to create a third.
The trinity is not just an aspect of God but of us. Each of us had a mother and father and each of our children will have a mother and father. We are made in God's image so we mirror this trinity of creation.
If the universe were only chaos, nothing could come together and form life. If the universe were only order, nothing could come apart and form life. Without order, our bodies couldn't hold together or continue its functions so there could be no life, yet without chaos we would have no food to eat or air to breathe or water to drink and there could be no life. It's the balance of creation and destruction that allows life: hence the trinity.