The Centerline Editor allows you to tweak and reshape a brush stroke by manipulating its centre line rather than its contour (you can manipulate its contour using the Contour Editor tool). This gives a flexibility similar to manipulating a pencil line with the Contour Editor tool.
Keep in mind that brush strokes are vector shapes with a fill. As such, the Centerline Editor must do guess work to figure out the centreline of your brush strokes, and apply deformations on its shape as you tweak its control points. The Centerline Editor will not be able to make a accurate centreline out of brush strokes that merge together, that look scrambled or that otherwise do not have a clear direction.
If you use the Centerline Editor to deform a closed brush stroke with a fill inside it, the fill will not be reshaped to fit the new shape of the brush stroke.