What is the difference between the New Testament and the Old Testament?

The Old Testament is a selection of books taken from the Jewish holy writings, the Tanakh, by the early Christian church leaders, who were familiar with the Tanakh. They assembled those selections for use with the New Testament as being the parts of the Jewish tradition that were thought to be relevant to the times around 200-300 AD.

The new Testament is the purely Christian writings describing the life of Jesus and including writings attributed to the Apostles on how a Christian and a Christian community, should behave.

Christians consider the Old Testament as a record of God's dealings with His chosen people, the Israelites, and the promise He made to them to bless the world through them. The New Testament records what Christians believe is the fulfilment of that promise, the birth of Christ, His life and the building of His church. Those of Jewish faith regard the Old Testament a selected portion of their Scripture. Those of Christian faith see both the Old and New Testaments as Scripture.

Testament means "covenant." Christian Bibles consist of the Old Testament and the New Testament.

Christians believe the fulfilment of the law was accomplished by Christ's death and resurrection. Believers consider themselves not under the Old Testament law, but that by grace with the help of the Holy Spirit they follow the Law of Christ (Galatians 6:2) which is "Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. This is the first and great commandment. And the second is like unto it, Thou shalt love thy neighbour as thyself. On these two commandments hang all the law and the prophets." (Matthew 22:37-40)

Other Notes
Some believe Testament means "truth telling" or something that serves as written truth and that it is not a synonym for "covenant".

The New Testament is an account of the birth, the active ministry, and death of Jesus Christ and the works and writings of his apostles after his death.

The Old Testament is a collection of 39 books of history, poetry, advice and prophecy, and is considered sacred by Jews and Christians alike. The New Testament is 27 books, containing four accounts of Jesus life and teachings, an account of the early church's activities, and numerous letters from church leaders to individual congregations, containing teachings and advice. It finishes with a single book of prophecy regarding the end of the world as we know it, and the coming of God's eternal Kingdom. It is considered sacred to Christians alone..