A Section, or sectional, is a drawing. A "sideways" view of the sets, lights, rigging, and theatre structure itself. This drawing is done typically to provide information to designers so that they can reference how the different elements are going to, positionally, relate to each other.
A center line sectional is achieved by establishing an imaginary "plane" through the centerline of the theatre and perpendicular to the stage floor. Then drawing a "view" showing the thicknesses, heights, and up/downstage positions of all the elements of the set as it relates to the theatre. Typically a Scenic Designer will provide a "section" to the TD who will hand it off to the Lighting Designer. The Lighting Designer will then use the Section to establish things such as Trim heights for electrics, and to determine the angle at which lighting instruments will be focused to hit various parts of the stage and/or scenic elements.
A centerline section will usually be labeled as "C.L. Looking Stage Right" or "C.L. Looking Stage Left." Here is one fairly complex example.
"Vertical Section through CenterLine" is a common and correct name for such a drawing. Centerline sections are often referred to as "cross sections", although a "Cross Section" could be a section drawn through any number of infinite points along the SL to SR axis of the theatre, or the "Y" Axis of any individual scenic element. A "Cross Section" could also denote a sectional view of anything drawn along any number of infinite planes the exact orientation would need to be denoted somewhere on the drawing to allow the reader to properly identify the view. Other sections are often denoted by the insertion of a dashed, not dotted, line running through and area of the set on the ground plan. Often Designers will provide sections of particularly intricate areas of the set or of flats to denote styles and positions of Moldings.