Praise be to Allaah.
Bleaching the skin is done for one of two reasons:
it is done in the pursuit of beauty and perfection. This is not permitted because it involves changing the creation of Allaah, and because it is regarded as being in the same class as tattooing, practitioners of which were cursed by the Messenger of Allaah (peace and blessings of Allaah be upon him).
It is done to remove a fault of blemish, such as a black spot or something similar on the hand or elsewhere, which a person bleaches in an attempt to remove the blemish. There is nothing wrong with this, because it is counted as removing faults. And Allaah knows best.