What does the CLEAN badge mean in iTunes?
It is opposite to the Explicit version of a song, which may contain profanity or other unacceptable language. I do assume these don't have bad words in the text, etc. Unlike Explicit, which are more "clean" from author's point of view — they aren't "beeped" over phrases inappropriate before certain ages.

BTW there are several threads on Apple.com about people losing their Explicit versions after Music Match, just because songs are the same but Apple hasve a Clean version of it.