In chapter 3 of The Strange Case of Dr. Jekyll and Mr. Hyde we find Dr. Jekyll giving one of his well-known society dinners where the cream of the crop is always invited. Utterson was there as always, only this time he had in mind one thing: the will of Dr. Jekyll. As we know, by now Jekyll has expressed a strong interest in Mr. Hyde (his chemically and supernaturally-induced alter ego), for which he asks Utterson to accept the fact that he wants "poor Hyde" to get everything in his will. Utterson's loyalty to Jekyll drives him to reject this plan but Jekyll insists. The fact that Utterson insists further and does not want to hear anymore nonsense about the "painful relationship" that Jekyll describes to have with Hyde, he gets compared to Dr. Lanyon, who was he first recipient of the hidebound insults.
Jekyll had compared Utterson with the disapproving Dr. Lanyon, who had expressed to Utterson his concerns and disappointment regarding Jekyll's own view of the practice of medicine, science, and experimentation. Since Utterson expresses to Jekyll a genuine, conservative concern regarding Jekyll's finances, the latter retorts that Utterson is acting like Dr. Lanyon, who is a "hidebound pedant".
Granted, Jekyll first calls Lanyon a "hidebound", and then uses this adjective with the other, "pedant". The "hidebound" epithet refers to the persistence of Dr. Lanyon to stick to the canons of the ethical practice of science and medicine. Jekyll thinks Lanyon is too conservative and stuck up in his ways to fully understand Jekyll's ideas.
However, Jekyll actually has a degree of resentment against Lanyon and, for this reason, gets overly excited talking about him to the point of calling him a "hidebound pedant". That's two insults now, not just one!
[Lanyon is] an ignorant, blatant pedant. I was never more disappointed in any man than Lanyon.
This contradicts the words that Jekyll had just pronounced before calling the man a "pedant", which is someone who is haughty, annoying, and hard to like. He had claimed to still like the Doctor, after all.
We know, as readers, that in trying to create two different people out of one, what Jekyll ends up really doing is diluting himself, or even both personalities as one tries to get a stronger hold of the other. This emotional moment gives way to the ups and downs in behavior that Jekyll would be experiencing as a result of his crazy experiment.
If you break down the phrase into the two words, it's easier to figure out.
Hidebound or hide-bound means someone who is extremely conservative or inflexible. A pedant is someone who makes a show of their knowledge.
A hidebound pedant is a very conservative, inflexible person who lets everyone know how smart they are. Not a very charming personality, to say the least!
Check out the definitions linked below to get some other shades of meaning in the words.