If someone has an incurable disease, they cannot be cured of it.
He is suffering from an incurable skin disease.
他身患一种无可救治的皮肤病。
You can use incurable to indicate that someone has a particular quality or attitude and will not change.
Poor old Willy is an incurable romantic.
可怜的老威利是个无可救药的浪漫主义者。