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."