The popular saying that 危机 = 'danger + opportunity' is a slight oversimplification, but it's a useful mnemonic. The 机 here means 'crucial juncture' rather than 'opportunity,' but the idea of a turning point is accurate.
usage
Common compounds: 金融危机 (financial crisis), 经济危机 (economic crisis), 中年危机 (midlife crisis), 危机感 (sense of crisis).
