-인데 is one case of the -ㄴ데 form of an adjective: 이다 (is) + -ㄴ데 -> 인데. For verbs, it becomes -는데. It has two major related uses: 1) "even though" or "when" (a mild contradiction), and 2) "when", "just as" (describing an unexpected event). - 유명했던 가수인데 지금은 아무도 모른다 = Although he's a singer once famous, no one knows him now. - 여름은 여름인데 덥지가 않다 = It is summer all right, but it is just not warm. - 오늘 야외 행사 할 건데 비가 온다 = We have an outdoor event today but it is raining. - 왜 서두를까. 시간도 많은데. = I wonder what the rush is. When there's plenty of time. - 자고 있는데 총소리가 들렸다 = I heard a gunshot while I was sleeping. (meaning-2)