Despair is the condition of being at a loss without seeing a way forward, especially under severe trouble. Biblical usage distinguishes being perplexed or pressed from being utterly driven into despair.
In 2 Corinthians 4:8 Paul describes believers as perplexed but not unto despair—at a loss, yet not utterly at a loss. Related expressions describe something incurable or a condition regarded as beyond remedy.
The New Testament expression intensifies the idea of being at a loss through a prefix meaning utterly or completely. Related Old Testament words can mean incurable or sick, including descriptions of an incurably wicked heart.