Feasts to honor the Trinity, though not part of the liturgical calendar used for the Mass, were included locally in the Divine Office from the time of Gregory the Great as the Office of the Holy Trinity, with their own canticles, responses and hymns.
The doctrine of the Trinity is a central tenant of the Catholic faith and is excepted by most, but not all, of the other Christian faiths. This is revealed Truth which man could not come to through understanding of natural law. Though in Scripture there is no single term by which the Three Divine Persons are denoted together, they are separately described in several places. In Matthew 28:18 Jesus tells the disciples:
...go and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit.
In Luke (1:35) Scripture tells us:
And the angel said to her in reply, "The Holy Spirit will come upon you, and the power of the Most High will overshadow you. Therefore the child to be born will be called holy, the Son of God.
The Most High is the Father, described by a phrase used in the Old Testament, as in Sirach(Ecclesiasticus) 24:
Wisdom sings her own praises, before her own people she proclaims her glory;In the assembly of the Most High she opens her mouth, in the presence of his hosts she declares her worth:"From the mouth of the Most High I came forth..
The references to the Holy Spirit and the Son are clearly stated.
The early Church from Apostolic times taught the doctrine of the Trinity. The baptismal formula is ancient. It had its origin in the oral tradition that became Scripture and it's use predated Scripture.
At the time of the Arian Heresy in the fourth century, the Trinitarian dogma was already encapsulated in the doxologies in use:
Glory to the Father, through the Son and in the Holy Ghost.
carried through to the present day as
Glory to the Father, Son and Holy Spirit
There are many passages in the ante-Nicene (that is before the Council of Nicene) Church Fathers which attest to the wide spread belief in the dogma of the Trinity; St. Basil tells us that when Christians lit the evening lamp it was their custom to give thanks to God with Prayer
We praise the Father, and the Son, and the Holy Spirit of God
This is the consistent teaching of the Church Fathers.
In theological terms the Trinity can be described as a mystery. Theologically a mystery is a Truth which we are not only incapable of discovering apart from Divine Revelation, but which even when revealed remains hidden. That is it is a fact so enveloped by an aspect beyond our understanding that even when revealed it is necessary that it's acceptance be a manifest matter of faith. It is, in short, impenetrable to reason, although it contains no intrinsic impossibility which violates the laws of nature. It is incomprehensible, as God will alway be incomprehensible to us on a fundamental level. I leave you with St Jerome who said:
The true profession of the mystery of the Trinity is to own that we do not comprehend it.