The phrase structuring element comes from mathematical morphology, the formal field that gave us dilation, erosion, opening, and closingLoading.... The small shape is what gives the operation its structure. The same dilation produces a very different result with a small square than with a long horizontal line.
Most BOM users never type the phrase. The morphological operations expose the structuring element as Kernel radius (px) and Kernel shape (default Disk) parameters in the GUI, and Top-hat exposes only Kernel radius. Pick a radius and a shape, and the engine builds the element for you. The term is useful when you read the Engines Reference, or when an unexpected result comes from a structuring element whose shape did not match the structures you were trying to find.