Most many-god religions [like Hinduism] (polytheism) have a head god, sort of a chairman of the board. The religions with which we are most familiar have only one God. Jews give him the personal name, Yahweh or Jehovah (but it is too holy to say; so they call him Lord), and Muslims call him Allah (which just means God). Christians, although claiming to worship one God, talk about a "triune" (three in one) God and speak of Trinity (26th of May) (threeness in unity): Father, Son and Holy Spirit. Several religious groupings have mulled over the idea of Trinity but have given up and decided that there is only the one deity. Some hold that Jesus is just a human being whose reputation became blown out of all proportion (Unitarians). Or else he is just some other form of created being, something like an angel, whom God assigned the task of undoing Adam’s sin (Jehovah’s Witness). Others have gone in the other direction and declared that Father, Christ and Spirit are three different gods (Mormons).
Dismissal of Trinity shows how hard the idea is to understand. In bad moments some Christians, too, wonder if the whole doctrine is a nonsense that our ancestors spouted when they had nothing better to do.
Trinity is not merely hard to understand. It is impossible! Still, we can catch glimmerings and can point in the general direction of meaning. Please do not imagine that all difference is bad, and that we must toe a rigid doctrinal line. There is plenty of flexibility within Trinity. For example, think of yourself as you have grown. How you pictured God when you were five years old is not how you understand him now [we hope!]. Moreover, what you learn of God in 20 or 50 or 90 years will cause you to think of him in still different ways. We grow in our relation with God just as we do in our relations with people around us because God made us like him: A God of relationships.
There are many reasons why different people think of God in different ways. Some people are task-oriented (wanting to get things done). Others are people-oriented (how they relate to others is more important for them). Some are conscious of colour and form and music. Others are moved by language; the written and spoken word and its beauty. And there are those who are moved by the wonders of the natural world; still others have not an artistic bone in their body. All these things affect how we like to think of God, and God doesn’t care so much how we think of him — as long as we continue growing in faith and understanding. But don’t worry too much if you cannot understand because God is infinite. He cannot be defined. He cannot be understood; St Augustine said, "If you can understand it, it's not God." But God can be known in a personal way.
The word "Trinity" doesn’t actually appear in the Bible. It was first used in the Church in 181 AD. It is shorthand for teaching that is definitely in the Bible, particularly in the New Testament. The key passage is Matthew 28:19. Jesus said, "Go therefore and make disciples of all the nations, baptising them in the name of the Father and of the Son and of the Holy Spirit…" Note that the word "name" is singular, for God is one. God is a loving unity of Father, Son and Holy Spirit. In other words God is one in three and three in one. The Church teaches that God has always been and will always be Father, Son and Holy Spirit. The Son [or “Word” as St. John would put it] became a human being, not as if he stopped being the eternal Son of God, but by taking up human nature into his divine nature. Jesus is truly God and truly man.  Since Jesus is truly God, his sacrifice on the cross is infinitely precious, outweighing all the sins of the world. Since Jesus is truly man, he has lived and died on our behalf and in our place. Since Jesus is both God and man, divine and human, he has conquered death by dying in his human nature and by rising again on the third day.
There have been some simple traditional images of the Trinity that help us to accept that God is one in three and three in one. (a) St Patrick used a clover leaf or shamrock to show the oneness and the threeness of God. (b) An equilateral triangle shows that Father, Son and Holy Spirit are one and equal. Remember that the Trinity is undivided and therefore each Person cannot be regarded as one-third of the whole. (c) One's own personal unity of will, memory and intelligence shows that every human being is one in three and three in one. After all, God made us in his own image.
St Anselm [approx. 1033 - 1109 Archbishop of Canterbury 1093-97 & 1107 - 1109] wrote that he believed so that he might understand. Without faith in the heart of the reader, the Bible does not seem to make a lot of sense. Faith is not only trust in God and Christ but also obedience to God's commandments. Without obedience to the commandments, one cannot really make sense of the Bible. Faith and obedience result in a personal relationship to God and therefore in a prayer life. A personal relationship to God involves a personal relationship to others. And the Trinity is about God “internally” having these possibilities of personal relationships: Father, Son and Holy Spirit.
Trying to delve into the very essence of God was never going to be easy!