A 아니면 B = A or B; between two questions
or, otherwise, if not
Example
커피 마실래요, 아니면 차 마실래요?
Would you like coffee, or tea?
Word parts
아니다 'to not be' + -면 'if' — literally 'if not'.
Good to know
아니면 is the everyday 'or' between questions; 또는 is more formal or written.