Some time before the events of the game, Mephiles the Dark was sealed by a time-traveling Shadow the Hedgehog inside the Scepter of Darkness, which was given to him by the dying Duke of Soleanna. However, he left it at Soleanna in the open, citing that he "knows what will happen to it anyways." It eventually came into the possession of Doctor Eggman, and Rouge the Bat was sent to steal it from him. Shadow (before he had traveled back in time) went to rescue Rouge, and during their escape, the Scepter was broken, which resulted in the release of Mephiles.
Some time later, Shadow and Rouge came across an archaeologist called Adrianna who was studying the Scepter, and after saving her from an attack by Iblis' minions, she read to them an ancient text she discovered about the Scepter and Mephiles, although she was unable to comprehend its meaning. After that, the two constructed a new Scepter so that they could re-imprison Mephiles, but it was no longer effective in sealing him because he had grown too powerful from the Chaos Emeralds, combined with the present Mephiles absorbing the Shadow of ten years prior's shadow. The new Scepter was also shattered and rendered useless.
Interestingly, when Rouge returns from the future, a G.U.N. soldier calls it the "Book of Darkness" over her intercom, but the in-game subtitles still refer to it as a Scepter. This is likely a recording error.
When the Scepter was broken, it disabled all of Eggman's robots around it. This, along with Eggman's order to fall back when it was destroyed, implies that electromagnetism may have been part of the Scepter.