That means it is sick! Have you tested you water recently? If not you need too, just to make sure that there isn't a problem in your water!
Usually when a fish has stuff trailing out of it like that means there is a problem. Most likely the fish was sick when you got it. How long have you had it? Did it eat at all since you've had it? When you go to the LFS
look at the fish carefully make them feed the fish and see that it eats before you buy it! A clown is a tough fish but if it isn't eating that isn't a good sign. I always get worried when I see one of my fish not eating. I just lost a green chromis tonight infact...the fish wouldn't eat yesterday when I fed and I knew that something was wrong. I'm not sure what to do about it but I do know that there is a problem!.....Sorry...I hope things work out with your clown!