Kosher just means it is fit for human consumption according to Jewish law. Ef can probably tell us more about that.
In order to be called Kosher, it has to BE Kosher and there are many states in the U.S. that have laws of "truth in labeling" on that subject.
The laws regarding Kosher are many and complex, depending on what food items you are dealing with. Generally speaking, before manufacturers or packagers label something as kosher, they make sure that their product has rabbinic supervision to assure that it really meets the requirements.
As far as kosher honey requirements, they are relatively simple: the honey has to be pure, with no additives of animal origin. That can be a problem with comb honey if it is infested with eggs of wax moths or other insects that tunnel beneath the cappings. I have seen comb honey that looked beautiful when packaged and a few weeks later turned out to be infested. That, of course, means it wasn't kosher from the outset. People who eat only kosher foods can use regular extracted honey that has been filtered, even though it doesn't have supervision. However, some people will still only purchase honey that is labeled as kosher and gives the assurances of reliable, rabbinic supervision.
As an example, in years gone by, when I marketed honey, people who know me, would buy my honey without any hesitation. However, there arre those who don't know me and some would and some wouldn't buy my honey. On the other hand, my grandson, who markets on a much larger scale, in order to assure acceptability by all, has arrranged for supervision which enables him to label his honey as "Kosher" and his labels bear the insignia of the authority who testifies to it's being authentically kosher.