What is "New Jerusalem" from the New Testament?
The New Jerusalem described by John in the Book of Revelations was not an idea of his own invention. On the contrary, while Revelations portrays the city using the same fantastical imagery that characterizes the rest of the book, the writer draws heavily upon an idea of New Jerusalem almost as old as Judaism itself. In the Old Testament, this place is referred to as "Zion."
Both Zion and New Jerusalem seem to signify a physical place which is, at the same time, an ideal state for the Jewish people, longed for and prophesied. Christians and Jews alike have long set stock by the physical possession of Jerusalem, but "New Jerusalem" represents not only the city itself, but a time when it will be inhabited entirely by God's faithful, safe from attack and foreign occupation. In Revelations 21:15-17, John describes "The Holy City, the new Jerusalem, coming down out of heaven from God, prepared as a bride beautifully dressed for her husband," the world having been wiped clean and recreated again following the apocalypse and the re-gathering of the faithful by Christ.
Apart from the discussion of the New Jerusalem in Revelations, it is also mentioned in the New Testament by Jesus, who also refers back to older prophecies to give some indication of when New Jerusalem will come about. In Matthew 24 (and indeed in Mark 13 and Luke 21), Jesus prophesies that the Temple at Jerusalem will be destroyed, and that this will be a sign of the end of the age. After this, The Son of Man will return, and the New Jerusalem will be on its way. Notably, the Temple was destroyed in AD 70, which led to a belief among the early Christians that the apocalypse would be soon in coming.
Although not all Christian sects agree on the nature of the New Jerusalem, this city is a major part of Christian eschatology. The New Jerusalem is, essentially, heaven.
If the book of Revelation is to be taken literally, the New Jerusalem will be a city that is a perfect cube with dimensions of about 1400 miles on each side. The city is to be made of all sorts of precious stones and of gold. Most importantly, the New Jerusalem is to be a place in which the saved will live with God. He will actually live with "his people." In this city there will be no day and night because the glory of God will provide constant light forever.
In a nutshell, then, the New Jerusalem is heaven come down to Earth.