“After Easter, the Solemnity of Pentecost is the second most important day in the Church year.”
Bishop Peter J. Elliott, Ceremonies of the Liturgical Year 325
If Pentecost outranks Christmas on the Liturgical Calendar (or, I know it might be argued, is equal to it) then why is it that Christmas has an Octave but Pentecost does not? It appears that even the pope who approved the elimination of the Octave of Pentecost had no idea what was going on. Fr. Z explains what a Liturgical Octave is and tells the story of the Octave of Pentecost in a podcast found here.
On the older Liturgical Calendar the Octave Day of Pentecost is Trinity Sunday. This is always a great time of year to re-familiarize yourself with what the Catholic faith teaches us about the Holy Trinity:
The mystery of the Most Holy Trinity is the central mystery of Christian faith and life. It is the mystery of God in himself. It is therefore the source of all the other mysteries of faith, the light that enlightens them. It is the most fundamental and essential teaching in the “hierarchy of the truths of faith”. The whole history of salvation is identical with the history of the way and the means by which the one true God, Father, Son and Holy Spirit, reveals himself to men “and reconciles and unites with himself those who turn away from sin”.
The Trinity is a mystery of faith in the strict sense, one of the “mysteries that are hidden in God, which can never be known unless they are revealed by God”. To be sure, God has left traces of his Trinitarian being in his work of creation and in his Revelation throughout the Old Testament. But his inmost Being as Holy Trinity is a mystery that is inaccessible to reason alone or even to Israel’s faith before the Incarnation of God’s Son and the sending of the Holy Spirit.
and it is a great time to recite the Athanasian Creed.