What is the lake of fire?
The lake of fire is the place of everlasting fire and brimstone where Satan, the beast, the false prophet, death, hell, and all whose names are not written in the book of life are finally cast; it is called the second death and burns forever with unending torment.
Scripture shows that the beast and the false prophet are the first to be thrown alive into this lake of fire and brimstone at the Battle of Armageddon. When the thousand years are finished and Satan is loosed for the last rebellion, he too is defeated and "cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever."
After that comes the judgment before the great white throne, where the dead, small and great, stand before God and are judged out of the books according to their works. At that time "death and hell were cast into the lake of fire. This is the second death." Anyone whose name is not found written in the book of life is likewise cast into the lake of fire.
This teaching is given plainly, without softening: hell and the lake of fire are literal, and the torment there is everlasting, day and night, forever and ever. It is described as the final destination for the devil, the beast, the false prophet, death itself, hell itself, and every person not written in the book of life.
The scriptures
And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone.
And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
And death and hell were cast into the lake of fire. This is the second death. And whosoever was not found written in the book of life was cast into the lake of fire.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.