It means "no matter how ... you are/he is/it is. You/He/It still ..." Here are some examples. 네가 아무리 잘해도 그렇지. 연습을 꾸준히 해야지. (Sure, you're really good. But still, you need to continue to practice.) 네가 그 친구랑 아무리 친해도 그렇지. 그렇게 함부로 대하면 안 되지. (Sure, you are really close to that friend. But still, you shouldn't treat her like that.) 그게 아무리 예뻐도 그렇지. 그건 너무 비싸다. (Sure, that's really pretty. But that's just too expensive.)