our A: You and I live in a three-dimensional world. All physical objects have a certain height, width, and depth. One person can look like someone else, or behave like someone else, or even sound like someone else. But a person cannot actually be the same as another person. They are distinct individuals.
God, however, lives without the limitations of a three-dimensional universe. He is spirit. And he is infinitely more complex than we are.
That is why Jesus the Son can be different from the Father. And, yet the same.
The Bible clearly speaks of: God the Son, God the Father, and God the Holy Spirit. But emphasizes that there is only ONE God.
If we were to use math, it would not be, 1+1+1=3. It would be 1x1x1=1. God is a triune God.
Thus the term: "Tri" meaning three, and "Unity" meaning one, Tri+Unity = Trinity. It is a way of acknowledging what the Bible reveals to us about God, that God is yet three "Persons" who have the same essence of deity. Some have tried to give human illustrations for the Trinity, such as H2O being water, ice and steam (all different forms, but all are H2O). Another illustration is an egg having a shell, egg yolk and egg white, but this egg illustration shows that there would be "parts" to God, which isn't the case.
God the Son (Jesus) is fully, completely God. God the Father is fully, completely God. And God the Holy Spirit is fully, completely God. Yet there is only one God. In our world, with our limited human experience, it's tough to understand the Trinity. But from the beginning we see God this way in Scripture. Notice the plural pronouns "us" and "our" in Genesis 1:26 -- Then God said, "Let us make man in our image, in our likeness, and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground."
Though not a complete list, here is some other Scripture that shows God is one, in Trinity:
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