Have you ever seen a cartoon showing the top of a person's head cut aroud the top and flipping up and down, like a door? It opens and input (knowledge) goes into the mind (brain) and then closes. Since it acts like a lid, it has hinges to hold it on the head.
To "blow the hinges off one's mind" means that something has entered the mind and was so exciting, profound or wonderful, that it "blew your mind" - even the hinges that held the top of the head.