To destroy utterly, to cause to perish, to lose. In the middle voice, 'to perish' — to be ruined or lost. Apollymi covers a wide range: physical death, spiritual ruin, and the loss of something valuable. It is the dark counterpart to sōzō (to save).
The word appears in some of the most dramatic NT statements. John 3:16 presents the stark alternative: believe and have eternal life, or perish. Jesus came to seek and save the lost (Luke 19:10) — same root. The parables of the lost sheep, coin, and son all use apollymi. Paul warns that the message of the cross is 'foolishness to those who are perishing' (1 Corinthians 1:18). Salvation and destruction are the two roads.