An adverb used with a negative verb (二度と〜ない) meaning never again; indicates a strong determination that something will not happen or be done again.
彼には二度と会わないと決めた。
I've decided I'll never see him again.
そんな失敗は二度と繰り返さない。
I will never repeat that kind of mistake again.
二度とここには来ないでください。
Please never come here again.