To be a Catholic is to have the mind of the Catholic Church, the Sensus Ecclesiae, to submit to the teaching, the morals, the liturgy and the discipline of the Catholic Church. Faith is a submission of the intellect to the truth revealed by God and proposed by His Church.
As we have seen in the readings of the Second Sunday of Lent, God the Father orders us to listen to His Divine Son who passes on to us the Truth He Himself received from His Father. Jesus, in His turn, orders His Apostles to go and teach all nations whatsoever He has taught them. He who hears them hears Him, he who rejects them, rejects Him. It is clear. The Apostles are one with Our Lord, they are His ambassadors. The Church is the Mystical Body of Christ.
They taught the very same things to their own disciples and the chain of Tradition has thus been linked ever since, until our own days, and will be so until the end of the world. That is also what is called the note of apostolicity: the unbroken chain of teaching and of the succession in the hierarchy.
Here are some famous texts to prove how Tradition was understood in the first centuries on different aspects of the faith, the morals, liturgy. It helps to know these things today; it strengthens our own faith, since we are part of this uninterrupted chain, this apostolic faith.
St Paul’s famous text to the Galatian (about 53 A.D.) is a revealed landmark:
“But though we, or an angel from heaven, preach a gospel to you besides that which we have preached to you, let him be anathema. As we said before, so now I say again: If any one preach to you a gospel, besides that which you have received, let him be anathema. (…) For I give you to understand, brethren, that the gospel which was preached by me is not according to man. For neither did I receive it of man, nor did I learn it; but by the revelation of Jesus Christ.” (Gal 1:8-12)
St Ireneus wrote around the year 180 A.D., in his book Against the Heresies about tradition and the necessity of apostolic continuity:
“But, again, when we refer them (the heretics) to that tradition which originates from the apostles, [and] which is preserved by means of the succession of presbyters (bishops and priests) in the Churches, they object to tradition, saying that they themselves are wiser not merely than the presbyters, but even than the apostles, because they have discovered the unadulterated truth. For [they maintain] that the apostles intermingled the things of the law with the words of the Saviour; (…) It comes to this, therefore, that these men do now consent neither to Scripture nor to tradition.
“It is within the power of all, therefore, in every Church, who may wish to see the truth, to contemplate clearly the tradition of the apostles manifested throughout the whole world; and we are in a position to reckon up those who were by the apostles instituted bishops in the Churches, and [to demonstrate] the succession of these men to our own times…
“(…) tradition derived from the apostles, of the very great, the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul; as also [by pointing out] the faith preached to men, which comes down to our time by means of the successions of the bishops. For it is a matter of necessity that every Church should agree with this Church, on account of its preeminent authority…”
“(List of the first Popes, Linus, Anacletus, Clement, etc. up to Eleutherius -- the pope reigning then) In this order, and by this succession, the ecclesiastical tradition from the apostles, and the preaching of the truth, have come down to us. And this is most abundant proof that there is one and the same vivifying faith, which has been preserved in the Church from the apostles until now, and handed down in truth.” (Book 2, chapters 2 and 3) http://www.newadvent.org/fathers/0103302.htm