StructuredSelection is an option for cells that determines whether to allow only complete subexpressions be selected interactively in a typeset cell.
StructuredSelection is more often set at a global level than at the level of individual cells. It applies only to typeset, i.e., BoxData cells.
With the setting StructuredSelection True, you can only select a complete subexpression in a typeset cell. If you try to extend the selection by pressing , for instance, the selection changes in discrete jumps, moving directly to the next higher subexpression.
With the default setting StructuredSelection False, if you extend the selection by pressing , the selection advances by a single character.
See The Mathematica Book: Section 2.11.11.
See also: Selectable, DragAndDrop.