- Tattoos and nail paint would be forbidden.
- The most shameful form of execution would be cutting off the hands or slitting the wrists.
- Hand models would be on par with Pornstars.
- Rings could be a sign of submissiveness or an extremely strong bond.
- Finger food would be seen as the most disgusting food possible on par with slugs.
- Writing would be more in the style of blurry symbols, able to be made without tools.
HereAnd here are a few reasons why
Religious views - In the early pilgrim days, a woman's hair was thought to distract men from thoughts of god and make his mind go to... less savoury areas, thus they kept their covered when in church. The same could be said of hands; soft, delicate hands may be though of as so beautiful that a man who see's a ladies hands is overcome with... thoughts. Alternatively, if their god used his hands to form them (or something to that effect), they might see hands as such a godly trait that they would disgrace him by showing their hands.
Magic - Perhaps in this world, magic exists but is forbidden. Thus having your hands covered works as an anti-magic counter spell.
Biology - If they're not human, maybe this species reproduces with their hands and thus common decency has it so that they cover the goods. there are many species that reproduce using limbs and some even remove those limbs.