The four marks of the church are one, holy catholic and apostolic. The Church which Jesus founded needs to be able to be identified. It is by these four signs that the true church is identified. These four signs can be found both in the Bible and in the writings of the Early Church Fathers.
One – Bible
Jesus spoke several times of the importance of unity in His church. “I ask not only on behalf of these, but also on behalf of those who will believe in me through their word, that they may all be one. As you, Father, are in me and I am in you, may they also be in us, so that the world may believe that you have sent me." - John 17: 20 – 21. "And now I am no longer in the world, but they are in the world, and I am coming to you. Holy Father, protect them in your name that you have given me, so that they may be one, as we are one." - John 17:11. "I have other sheep that do not belong to this fold. I must bring them also, and they will listen to my voice. So there will be one flock, one shepherd." - John 10:16. In the gospel of John, Jesus is very insistent that the Church be one. He ties it in with the unity that He has with His Father. It makes a lot of sense that He would want His church to be unified, because otherwise it could not lead people to the one God. St. Paul also wrote to his converts about the importance of unity. "Because there is one bread, we who are many are one body, for we all partake of the one bread." - 1 Corinthians 10:17. "There is one body and one Spirit, just as you were called to the one hope of your calling, one Lord, one faith, one baptism, one God and Father of all, who is above all and through all and in all." - Ephesians 4: 4 – 6. St Paul speaks of the many kinds of and reasons for unity in the Church. There is only one God and one truth, and so the Church must also be one.
One – Church Fathers
The Church Fathers also understood that unity within the Church is key to its existence and mission.
So I did what I had to do, as a man devoted to unity. And I should add that, where there is division and anger, God does not dwell. - Ignatius of Antioch Epistle to the Magnesians 7 – 8
Having received this preaching and this faith, as I have said, the Church, although scattered in the whole world, carefully preserves it, as if living in one house. She believes these things [everywhere] alike, as if she had but one heart and one soul, and preaches them harmoniously, teaches them, and hands them down, as if she had but one mouth. - Irenaeus Against Heresies1.10.2
He can no longer have God for his Father, who has not the Church for his mother. - Cyprian of Carthage On the Unity of the Church §6
These Church Fathers clearly show that they understood the necessity of unity in the Church. God is the definition of unity, being three persons in one God, and so anything with His approval and stamp would have to be unified and show its unity publicly.
Holy – Bible
The true church of Christ is holy because it shows people the path to holiness. None of its members are perfectly holy, because all human beings are flawed and have free will and can and do choose to occasionally go against God's teachings. However, the individual failings of members does not diminish the truth of the Church's teachings on holiness or the holiness of its founder. “Christ loved the church and gave himself up for her, in order to make her holy by cleansing her with the washing of water by the word, so as to present the church to himself in splendor, without a spot or wrinkle or anything of the kind—yes, so that she may be holy and without blemish." - Ephesians 5: 25 – 27. St. Paul writes about the mission of the Church and its founder, to make people holy so that they can reach Heaven.
Catholic – Bible
Catholic means universal. The true church of Christ is universal because God wants everyone to be with Him in Heaven, and so He desires salvation for everyone. Jesus was particularly insistent that the gospel be preached to everyone right before His ascension. “And he said to them, “Go into all the world and proclaim the good news to the whole creation.” - Mark 16:15. “Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit” - Matthew 28:19. His last instructions to His apostles were to make sure that they knew He wanted the entire world to be evangelized. This was what He was most concerned about as He left – that no one be excluded from salvation.
Catholic – Church Fathers
In the earliest days of the Church, the known world was not as large as it is now, but the early church fathers knew that they were called to spread Jesus' gospel throughout the world.
The Catholic Church possesses one and the same faith throughout the whole world, as we have already said. - Irenaeus Against Heresies 1:10
[The Church] is called catholic, then, because it extends over the whole world, from end to end of the earth, and because it teaches universally and infallibly each and every doctrine which must come to the knowledge of men, concerning things visible and invisible, heavenly and earthly, and because it brings every race of men into subjection to godliness, governors and governed, learned and unlearned, and because it universally treats and heals every class of sins, those committed with the soul and those with the body, and it possesses within itself every conceivable form of virtue, in deeds and in words and in the spiritual gifts of every description. - Cyril of Jerusalem Catechetical Lectures 18:23
And if you ever are visiting in cities, do not inquire simply where the house of the Lord is—for the others, sects of the impious, attempt to call their dens ‘houses of the Lord’—nor ask merely where the Church is, but where is the Catholic Church. For this is the name peculiar to this holy Church, the mother of us all, which is the spouse of our Lord Jesus Christ, the only-begotten Son of God. - Cyril of Jerusalem Catechetical Lectures 18:26
These early Christian writers demonstrate that they knew about the idea of catholicity and universality. They knew that the true church of Christ would extend over the entire world and that any church in a place is only legitimate if it is following Jesus Christ and supported by the work of the successors of the Apostles.
Apostolic – Bible
In the New Testament, St. Paul speaks to Timothy about the passing on of the apostolic mission. “And what you have heard from me through many witnesses entrust to faithful people who will be able to teach others as well.” - 2 Timothy 2:2. St. Paul was chosen and called by Jesus to be an apostle, and he passed that ministry on to Timothy. In this epistle, he tells Timothy to pass on the ministry that he (Timothy) had received to others so that the gospel will never stop being preached. This is what the Church understands as an apostolic church. It was founded on the apostles and is passed on to their successors even to the present day.
Apostolic – Church Fathers
The early Church Fathers had a very clear understanding of the apostolic nature of the Church. As the close successors of the apostles, they could see how the idea of succession worked in practice and how it was necessary for the continued life and growth of the Church.
Where, therefore, the gifts of the Lord have been placed, there it behooves us to learn the truth, [namely,] from those who possess that succession of the Church which is from the apostles and among whom exists that which is sound and blameless in conduct, as well as that which is unadulterated and incorrupt in speech. For these also preserve this faith of ours in one God who created all things; and they increase that love [which we have] for the Son of God, who accomplished such marvellous dispensations for our sake: and they expound the Scriptures to us without danger, neither blaspheming God, nor dishonouring the patriarchs, nor despising the prophets. - Irenaeus Against Heresies, 4, 26, 2, 5; Ch. 26
Suppose there arise a dispute relative to some important question among us, should we not have recourse to the most ancient Churches with which the apostles held constant intercourse, and learn from them what is certain and clear in regard to the present question? For how should it be if the apostles themselves had not left us writings? Would it not be necessary, [in that case,] to follow the course of the tradition which they handed down to those to whom they did commit the Churches? - Irenaeus Against Heresies 3,4, 1
Our Apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned, and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry. - Clement of Rome Letter to the Corinthians 44:1
After the death of the tyrant, the [Apostle John] came back again to Ephesus from the Island of Patmos; and, upon being invited, he went even to the neighboring cities of the pagans, here to appoint bishops, there to set in order whole Churches, and there to ordain to the clerical estate such as were designated by the Spirit. - Clement of Alexandria Who is the Rich Man that is Saved?42:2
Far be it from me to speak adversely of any of these clergy who, in succession from the apostles, confect by their sacred word the Body of Christ and through whose efforts also it is that we are Christians. - Jerome Letters 14:8
These authors had a very clear idea that the succession of the apostles was very important for the church. They knew that only through apostolic succession could the message of Christ be faithfully transmitted and kept faithful to the truth.