The following few paragraphs are drawn from Frank Sheed's excellent introduction to the Catholic Faith, Theology for Beginners (Servant Books). Sheed had plenty more to say about the subject of the Blessed Trinity, both in this book and in his even more comprehensive Theology and Sanity (Ignatius Press), but this tasty will get you started.
I enthusiastically encourage all Catholics — indeed anybody of any background who wishes to better understand the Catholic Church's doctrine of the Trinity — to read both these books. Reading them, you will discover that, as Sheed put it, "The rewards for persistence are immense."
And for good measure, here is the old Catholic Encyclopedia's compact historical overview of the solemn feast day in honor of the Blessed Trinity:
Trinity SundayThe first Sunday after Pentecost, instituted to honour the Most Holy Trinity. In the early Church no special Office or day was assigned for the Holy Trinity. When the Arian heresy was spreading the Fathers prepared an Office with canticles, responses, a Preface, and hymns, to be recited on Sundays.In the Sacramentary of St. Gregory the Great (P.L., LXXVIII, 116) there are prayers and the Preface of the Trinity. The Micrologies (P.L., CLI, 1020), written during the pontificate of Gregory VII (Nilles, II, 460), call the Sunday after Pentecost a Dominica vacans, with no special office, but add that in some places they recited the Office of the Holy Trinity composed by Bishop Stephen of Liège (903-20). By others the Office was said on the Sunday before Advent.Alexander II (1061-1073), not III (Nilles, 1. c.), refused a petition for a special feast on the plea, that such a feast was not customary in the Roman Church which daily honored the Holy Trinity by the Gloria, Patri, etc., but he did not forbid the celebration where it already existed.John XXII (1316-1334) ordered the feast for the entire Church on the first Sunday after Pentecost. A new Office had been made by the Franciscan John Peckham, Canon of Lyons, later Archbishop of Canterbury (d. 1292).The feast ranked as a double of the second class but was raised to the dignity of a primary of the first class, 24 July 1911, by Pius X (Acta Ap. Sedis, III, 351). The Greeks have no special feast. Since it was after the first great Pentecost that the doctrine of the Trinity was proclaimed to the world, the feast becomingly follows that of Pentecost.