How can we understand the mystery of the Blessed Trinity as "three Persons in one God"?

Because it is a mystery, the Blessed Trinity is impossible to understand by reason alone. By faith we can affirm the truths about the Blessed Trinity that have been divinely revealed to us and handed down to us through Sacred Scripture and Sacred Tradition.  

The Blessed Trinity is the central mystery of the Christian Faith, the very source and light of all other mysteries of Faith.   As such, it is the most fundamental and indispensable truth of Christianity, one that has been revealed to the Church and articulated by her through her reflection upon Sacred Scripture and Sacred Tradition.  (Cf. CCC 234-250,252)

The Most Holy Trinity is one God in three divine Persons. The Father is God, the Son is God, and the Holy Spirit is God, and each is of the same divine "substance", "essence," or "nature."  They are differentiated as three Persons only in their relationship to one another:   "It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds." (Lateran Council IV [1215]: DS 804). Yet we ought not attempt to distinguish the three Persons of the Blessed Trinity by their perceived "functions," as though it is the Father alone who creates, the Son alone who redeems, and the Spirit alone who sanctifies. All three are united in will and share in all divine works.  (Cf. CCC 253-255, 257-267)

-The Didache Bible