What is word of mouth in the Catholic religion?

Answer 1

The statement refers to Sacred Tradition as one with Sacred Scripture, and is found in the writings of s. Paul to the Thessalonians:

"And we also thank God constantly for this, that when you received the word of God, which you heard from us, you accepted it not as the word of men but as what it really is, the word of God, which is at work in you believers." (1 Thes 2:13)

"So then, brothers and sisters, stand firm and hold fast to the teachings we passed on to you, whether by word of mouth or by letter." (2 Thes 2:15)

We read in the Catechism:

"Sacred Tradition and Sacred Scripture...are bound closely together, and communicate one with the other. For both of them, flowing out from the same divine well-spring, come together in some fashion to form one thing, and move towards the same goal...

Sacred Scripture is the speech of God as it is put down in writing under the breath of the Holy Spirit...and [Holy] Tradition transmits in its entirety the Word of God which has been entrusted to the apostles by Christ the Lord and the Holy Spirit. It transmits it to the successors of the apostles so that, enlightened by the Spirit of truth, they may faithfully preserve, expound and spread it abroad by their preaching.

As a result the Church, to whom the transmission and interpretation of Revelation is entrusted, "does not derive her certainty about all revealed truths from the holy Scriptures alone. Both Scripture and Tradition must be accepted and honoured with equal sentiments of devotion and reverence."

This is discussed in depth in the Constitution Dei Verbumon Divine Revelation which you may find at the link below.