下辈子 refers to the next lifetime or the afterlife in Chinese folk belief and Buddhism. You often hear it in emotional contexts where someone makes a wish, promise, or regret about a future existence — for example, '下辈子我要做你的家人' ('In the next life, I want to be your family'). It's a noun, not a temporal adverb, so it usually appears as the subject or object in a sentence.