It means that someone's action is not bad as their threats.

They're metaphors to a dog barking. I'm sure you know that dogs bark a lot to threaten each other. The 'bark' refers to the threats a person makes, and the 'bite' refers to what they can actually do when they attack. If someone's bark is worse than his bite, then he makes a lot of threats (barking like a dog) but cannot carry them out (his 'bite' is weak).

It simply means that "bark" is just another word for the way he or she speaks. E.g like if a girl shouts at you, that simply means "bark". While "bite" is more like the way she or he acts. E.g like when a boy punches you, that's "bite". That phrase is just used metaphorically instead of having to lengthen a sentence which could put the reader off. Therefore that is why: "someone's bark is worse than his bite" is a sentence. It's just simply there to shorten a sentence that the writer might try to describe a character in the book, for the reader. And usually it's used for situations like an argument, fights, etc... (negative things) or maybe there is some meaning that may be positive but that's all I know. Hoped that helped :)