The word Trinity is not found in the Bible. It's a term we use to describe the fact that, although there is but one true and eternal God, there are three distinct beings within the Godhead (God the Father, God the Son - Jesus, and God the Holy Spirit.)
The Three are co-eternal, co-equal, one in purpose, of the same spiritual essence or substance, all knowing, all powerful and everywhere present. They are separate in their personhoods in that God the Father is not God the Son (Jesus) or God the Holy Spirit and vice- versa. The Three, however, make up the one true and eternal God. We refer to this as the Trinity or tri-unity of God.
Moses wrote about this in the Old Testament book of Genesis.
This is what he wrote:
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." So God created man in His own image, in the image of God He created him; male and female He created them." 1
Note: God alone is the creator. No one assisted Him (not even angels which He created.) The words "Us" and "Our" mean more than one.
Jesus spoke of this in the New Testament of the Bible:
This is what He said:
"When the Counselor (God the Holy Spirit) comes, whom I (God the Son-Jesus) will send to you from the Father (God the Father), the Spirit of truth who goes out from the Father, He will testify about Me." 2
1 (Genesis 1:26-27)
2 (John 15:26, words in parenthesis are mine)