The New Testament was written in order to make it possible for humanity to receive spiritual salvation. In order to have the knowledge that would save us, we need to know who Jesus Christ was, what he did for us, and to accept His sacrifice for our sins. We have to know whom God is, our Creator, who knows best how we should live our lives. Paul explained how important it was to have specific spiritual knowledge.
For everyone who calls on the name of the Lord shall be saved . . . And how shall they hear without preaching? (And, we could add, how could they learn about God and study about salvation unless the New Testament was written - Romans 10:13 - 14, HBFV throughout unless stated)
Therefore, it is important for people to spread the good news, or gospel, of Jesus so that more people may believe in Him and accept His warning message about God's coming ruling government, the kingdom of God. For these reasons, Jesus wanted the gospel preached to all people throughout the world.
And He (Christ) said to them, "Go into all the world and preach the gospel to the whole creation" (Mark 16:15)
The New Testament provides humanity with saving knowledge, which the Old Testament does not fully possess, although the same God inspired both. Most importantly, spiritual salvation and eternal life can only come through Jesus and not by some other means or person, as Peter explained to his nation's leadership (Acts 4:12).
Similarly, Jesus Himself told His disciples on the night before He died that he was the ONLY way to God the Father and that he embodied truth and eternal life (John 14:6).
So if we do not know who Jesus who and what He did for us, we cannot be saved. True, mere intellectual knowledge about the facts of Jesus' life and identity as the Son of God and God the Son is necessary but not sufficient to produce salvation. We also need to emotionally accept and act on what we hear as well for it to be effective in saving us. After all, as James states, 'faith without works is dead' (James 2:26).
The New Testament reveals to humanity the purpose and meaning of life. The main purpose of life on this earth, when correctly lived, is to prepare us for the next life. We are supposed to become like God in character, as Christ tells us, "Therefore, you shall be perfect, even as your Father Who is in heaven is perfect" (Matthew 5:48).
We are also to become just like Jesus, who is God, until we all are unified by a singular faith and knowledge of Christ, "unto a perfect man, unto the measure of the stature of the fullness of Christ" (Ephesians 4:13). This set of twenty-seven books gives us knowledge that is crucial to living a happy life. Such information, however, cannot be known by human reasoning and sensory experience alone.
In conclusion, the New Testament was written in order to provide people with saving knowledge that tells them the purpose and meaning of life.