I heard someone ask a question similar to this, so I thought I'd look into it, and this is what I found. If anyone has any comments to make regarding the answer to this question please don't hesitate!
Why do Catholics believe that God is three Persons, called the Holy Trinity? How can God be three Persons and still be one God?
Catholics believe there is one God consisting of three distinct and equal divine Persons--Father, Son and Holy Spirit--because on numerous occasions God has described Himself thus. The Old Testament gives intimations that there are more than one Person in God. In Genesis 1:26, God says, ``Let us make man to our image and likeness.'' In Isaias 9:6-7, God the Father revealed the imminent coming into the world of God the Son. In Psalms 2:7, we read, ``The Lord hath said to me: Thou art my son, this day have I begotten thee.'' And in the New Testament, God reveals this doctrine even more clearly. For example, at the baptism of Jesus Christ, the Holy Spirit appeared in the form of a dove, and the voice of God the Father was heard: ``This is my beloved Son, in whom I am well pleased.'' (Matt. 3:16-17). In Matthew 28:19, God the Son commanded the Apostles to baptize ``in the name of the Father, and of the Son, and of the Holy Ghost.'' And in 1 Cor. 12:4-6, the Bible refers to God with three names: Spirit, Lord, and God-- corresponding to the Father, the Son, and the Holy Spirit.
Three divine Persons in one Godhead may be incomprehensible to the human mind, but that is to be expected. How can man fully comprehend God's infinite make-up when he cannot fully comprehend his own finite make-up? We have to take God's word for it. Also, we can satisfy ourselves as to the feasibility of God's triune make-up by considering various other triune realities. The triangle, for example, is one distinct form with three distinct and equal sides. And the clover leaf is one leaf with three distinct and equal petals. There are many physical trinities on earth, therefore a Spiritual Trinity, who is God in Heaven, is not against human reason--it is simply above human reason.