The Silver Chair refers to the "vile engine of sorcery" (an actual chair made of silver) that is fashioned by the Queen of Underland to contain Prince Rilian for the one hour per night that he returns to his senses. Of course, the enchanted Rilian doesn't realize he's under the power of the wicked queen, so he willingly allows himself to be bound to the chair at the prescribed time.
The title, then, is a shout-out to not just the chair, but also the deception that swirls around it when it comes to Rilian and his sanity. The chair kind of represents the whole problem of Rilian's enchantment, and deciding to free Rilian from it is the moment the whole story hinges on—in doing so, Rilian is able to return home just before Caspian dies, thereby ensuring solid leadership for Narnia.
The silver chair, then, is both part of the problem and part of the solution in this book. And the title gives us a heads-up to pay attention to this shiny seat accordingly. Thanks, title.