The rabbis of the Talmud discuss this question. The Mishnah states "that which comes from something which is not kosher is not kosher, and that which comes from something which is kosher is kosher." So, for example, the milk of a camel or the eggs of a vulture are just as unkosher as the camel and the vulture.
Why then, since bees are not kosher, is the honey of a bee permitted?
Honey consists of nectar, which bees gather, store and transport to their honeycombs. While in the bee, the nectar is broken down and transformed into honey by enzymes in the bee. But it is not actually digested by the bee. So the honey is not a product of the bee itself--as is milk.
One hundred percent pure, raw honey is kosher. When purchasing honey, be sure to check that it is certified as kosher by a reliable kosher agency, since non-kosher foods may have been processed on the same equipment, and non-kosher flavorings may have been added.
We have an interesting article on honey and its role in Judaism here: Honey. Let me know if this is helpful and if I can be of any further assistance.
Mrs. Rochel Chein