The "wheel" that this question is asking about can be found in the story's opening prologue:

No connection, you would agree. But things can come together in strange ways. The wood was at the center, the hub of the wheel. All wheels must have a hub. A Ferris wheel has one, as the sun is the hub of the wheeling calendar. Fixed points they are, and best left undisturbed, for without them, nothing holds together. But sometimes people find this out too late.

The prologue points out that the following story begins with three seemingly disconnected events. Mae Tuck heads toward the woods by Treegap in the morning. At noon, Winnie Foster decides to think about running away. Then in the evening, a strange man shows up at the Foster house. A ferris wheel is also made up of very dissimilar parts, yet they are all connected in order for the ride to work. As the center turns, it causes all of the other parts to be moved as well. This is like the woods near Winnie's house. The woods wind up being a point of convergence for all three of the previously mentioned characters. Mae and her family go there once every ten years. Winnie happens upon Jesse Tuck drinking from the spring, and the strange man has been hunting down the origin of the story he heard as a boy in order to market eternal life.

The "author's wheel," introduced in the Prologue, is an analogy of a Ferris wheel.  Up close, this wheel represents a circle of time (specifically a year).  But the bigger idea presented in this analogy is that the wheel represents the circle of life itself.

In the context of setting, the center, or hub, of the wheel is the "the wood," a dense forest near the village of Treegap which has no road leading through it.  This wood is described as having an appearance of an "otherworld" and is owned by the Fosters, who live at its edge.  At the end of the Prologue, however, the author presents a caution to the reader that gives insight into the deeper meaning of the center of the wheel.  She suggests that the hubs of wheels are fixed points and should be left undisturbed.  Thematically, this idea foreshadows the main point of the entire story.