What was Valjean hiding?
In Les Misérables while Cosette and Valjean are talking/singing, the grown up Cosette wants to know about Valjean's past. And why they are constantly on the run. She makes a movement to lift his cuff and he quickly pulls away - why does he do this?
ETA: I believe this is around the song "Attack on Rue Plumet"
Best Answer
He just doesn't want her to know about his past as a criminal and prisoner. While that may not be much of a problem for Cosette, this isn't the experience Valjean has made in the past. I'd say he is ashamed about his criminal past and just doesn't want her to know, even if he was convicted for such ridiculously small a crime and has done more than enough good to wash away his sins. His past still bothers and haunts him and he has made the experience (and is constantly told by society, and not the least by Javert) that a man cannot change himself or his past. So this is a dark stain on his past that, while it won't ever vanish, he at least doesn't want Cosette to know and to cloud her believes in him (even if that wasn't likely to happen).
Another factor may be that he doesn't want her to know the whole story, including that he is (or at least feels) responsible for Fantine's death, which is something he's probably never forgiven himself, even if he's done all the best for Cosette.
EDIT: If you're actually asking about a real "cuff" she wants to lift in a specific scene (which I don't remember too well), then this can still be seen in light of the above explanations. He was most likely hiding his prisoner "tattoo" that he didn't want her to see for the above mentioned reasons. Why she made the movement to lift it is another question, though. Maybe she was curious as she felt he was hiding something or maybe she even drew her own conclusions and was looking for a prisoner "tattoo" on purpose.
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