What is the book of life?
The Book of Life is the Lamb's heavenly register in which God recorded the names of all who would become heirs of salvation, and this was written before the foundation of the world.
Scripture describes the Book of Life as a register kept in heaven, a written record of the names of all who are to obtain eternal life. Revelation speaks of it directly: the one who overcomes will be clothed in white raiment, and Jesus says He will not blot that person's name out of the book of life, but will confess that name before the Father and His angels. Philippians 4:3 also refers to fellow laborers whose names are in the book of life, and Luke 10:20 speaks of the disciples' names being written in heaven, showing that even before the crucifixion, this record already existed.
What is striking is that this record was not started at conversion or at any point in earthly history. The names of those who would be heirs of salvation were written in the Lamb's Book of Life before God ever formed the world. God finished the works of creation and redemption in His purpose before He ever laid the foundations of the earth, so that everything that exists is only what He had already determined would be. Titus 1:2 speaks of eternal life being promised before the world began, and 1 John 5:7-11 shows that this record of eternal life given in the Son was written before the world was formed.
This selection was based on God's foreknowledge. He knew beforehand the disposition of every heart toward Him and, viewing all things in light of His redemption plan through the Lamb who was determined to be slain before the foundation of the world, He chose some for salvation. Acts 15:18 says that all His works are known to Him from the beginning of the world, and Romans 8:29-30 shows that those He foreknew He also predestinated to be conformed to the image of His Son. So those written in the Book of Life were fashioned for salvation in His sight long before they were ever born.
Yet the Book of Life is not simply a fixed, unchangeable list with no bearing on this life. Revelation 3:5 warns that a name can be blotted out of the book of life, which shows that being written there carries responsibility to overcome. Revelation 17:8 and Revelation 20:15 describe the final reckoning: those whose names are not found written in the book of life are cast into the lake of fire, while those whose names remain are the ones who inherit eternal life with God.
The scriptures
Paul, a servant of God, and an apostle of Jesus Christ, according to the faith of God’s elect, and the acknowledging of the truth which is after godliness; In hope of eternal life, which God, that cannot lie, promised before the world began; But hath in due times manifested his word through preaching, which is committed unto me according to the commandment of God our Saviour;
For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.
And this is the record, that God hath given to us eternal life, and this life is in his Son.
And I intreat thee also, true yokefellow, help those women which laboured with me in the gospel, with Clement also, and with other my fellowlabourers, whose names are in the book of life.
He that overcometh, the same shall be clothed in white raiment; and I will not blot out his name out of the book of life, but I will confess his name before my Father, and before his angels.
The beast that thou sawest was, and is not; and shall ascend out of the bottomless pit, and go into perdition: and they that dwell on the earth shall wonder, whose names were not written in the book of life from the foundation of the world, when they behold the beast that was, and is not, and yet is.
And whosoever was not found written in the book of life was cast into the lake of fire.
Notwithstanding in this rejoice not, that the spirits are subject unto you; but rather rejoice, because your names are written in heaven.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.