Cellophane is regenerated cellulose. Its purpose is mechanical: it protects a wrapper from handling in a shop, from its neighbours in a box, and from the pocket it travels in.
On or off in the humidor?
Both work, and the choice is a real trade-off rather than a right answer. Left on, moisture exchange is slower and steadier and the wrapper is protected. Taken off, exchange is faster and cigars share aromas more freely with each other and with the cedar — which is why keepers who age deliberately tend to remove it, and keepers who rotate stock quickly tend not to.
Why it turns yellow
Cellophane on older cigars often goes amber. That is the film reacting slowly with oils migrating out of the wrapper. It is an indicator of time passed, not of damage, and it cannot be produced artificially in any way that survives inspection.
Not every sleeve is cellophane
Some cigars ship in non-permeable plastic films, which do seal. The distinction matters, because a plastic-sleeved cigar left in a humidor is not being humidified at all.