This Feast is truly and really a mystery. Difficult to explain in words, but, more easily demonstrated by actions. The Holy Trinity, simply put, is the doctrine of the Church that teaches there is One God, but Three Persons—Father, Son and Holy Spirit. The Godhead is communal, yet, united, that is: One.
Like I said, talking about this mystery is more easily expressed by action. We make the Sign of the Cross, we bless ourselves, we make this sign before we eat, at the beginning of Mass, in the celebration of the Sacraments and even in how we pray: To the Father, through the Son (Jesus Christ), driven by the Holy Spirit. So, what we celebrate is an essential Christian teaching. It makes one distinctly Christian to use this Sign of the Cross to teach, show, express and manifest what we believe about God, Jesus and the Holy Spirit. They are all one God, but, Three Persons. This one God is Creator (the Father), The Redeemer (the Son), and the Sanctifier (the Holy Spirit).
It is difficult to explain, yet, always a doctrine not of explanation, but one of action. God has shown Himself to us, revealed a truth: He is One God—Father, Son and Holy Spirit!