Perish comes from the greek word, Apollumi which means, "to destroy to put out of the way entirely, abolish, put an end to ruin, to perish, to be lost, ruined, destroyed"
The Bible speaks of this abolishing or destruction in Rev:
11Then I saw a great white throne and him who was seated on it. Earth and sky fled from his presence, and there was no place for them. 12And I saw the dead, great and small, standing before the throne, and books were opened. Another book was opened, which is the book of life. The dead were judged according to what they had done as recorded in the books. 13The sea gave up the dead that were in it, and death and Hades gave up the dead that were in them, and each person was judged according to what he had done. 14Then death and Hades were thrown into the lake of fire. The lake of fire is the second death. 15If anyone's name was not found written in the book of life, he was thrown into the lake of fire.
Thus if you believe, you will not perish by beging thrown into the lake of fire. The lake of fire is death of the soul. That is, the individual will be completely destroyed and cease to exist.