In Sharon's dream world of Harry Barker, the Napier's Bones are much like their real world equivalent: an abacus created by John Napier in 1617 for the calculation of products and quotients of numbers. This abacus consists of a board with a rim and a series of rods or "bones". The user places Napier's rods in the rim to conduct multiplication or division.
However, according to the hacker-only version of Wikipedia (as opposed to the luddie-sanitized one familiar to most denizens of the Internet), an additional legend states that Napier also postulated a form of "universal algorithm", a single unifying mathematical formula to explain the known universe. A hacker possessing knowledge of this universal algorithm could, in theory, control literally anyone or anything by manipulating the mathematical formulas governing its existence. Napier supposedly encoded the secret of this universal algorithm into models of the Bones that he himself created. Fortunately (or unfortunately, depending on your point of view), all but one of the Napier's self-built sets of Bones have been lost or destroyed, with the last remaining set removed from public display for unspecified reasons.
Harry Barker and his friends postulated that rumors that the last set of Napier's Bones were held in an unnamed vault in Groklots could be connected to the fact that Dexter emptied a vault at the bank the same day that the bank was broken into. The children suspected Gnawthrylilees, either directly or via proxy, might be in pursuit of the Bones to restore himself to power and take over the world. This theory was eventually proven correct: Professor Quux, the quiet, stuttering Defense Against the Black Arts instructor, was really in league with Gnawthrylilees and secretly attempting to acquire the Bones. Harry and his friends managed to track the Bones to their hiding place deep within the castle of Hollerith's, where Professor Dumpingcore hid them within the Mirror of Awkandsed. Harry managed to extract the Bones from the Mirror (since, after all, he didn't really want them) and destroy them by crushing them beneath his feet. With the destruction of the last set of encoded Bones, it is assumed that the secret of the universal algorithm will be lost to the hacking world forever.