The early Christians, most of them Jews, had a problem. Here they had the Son of God, risen from the dead, and worthy of adoration like the Father they worshiped. The Son spoke of sending the Holy Spirit after his final departure, a Holy Spirit who had generative powers. (And he inspired them not only to speak eloquently, but also to perform miracles.)
With a situation like that, what could they conclude but what we know today as the Trinity? This is the mystery St. Patrick explained by picking up for all to see – a shamrock, or three-leaved clover. It withstood the test of time, and today trinity is a familiar word.
When we pray, however, we speak to only one of the three, and we are treated by all the same. Prayers are answered, as the Son predicted, and the Church uses as intercessors not only the Mother of Christ, but the various mortals who have been canonized as saints.