The statement 'Rien n'effacait notre histoire' means
Nothing erases our affair. In the word-by-word translation, the noun 'rien' plus the adverb 'ne'* means 'nothing'. The verb 'effacait' means '[he/she/it] erased, removed, rubbed out, wiped away'. The possessive adjective 'notre' means 'our'. The noun 'histoire' means 'affair, history, story'.
*The letter 'e' is dropped in front of a word that begins with a vowel or an unaspirated 'h'.