The phrase structuring element is technical jargon from mathematical morphology, the formal field that gave us dilation, erosion, opening, and closingLoading.... The naming comes from the idea that this small shape is what gives structure to the operation — the same dilate engine produces a totally different result depending on whether the structuring element is a small square or a long horizontal line.
The good news: most BOM users never type the phrase. The morphological operation engines expose the structuring element as size and shape parameters in the GUI — pick a size, pick a shape, the engine builds the structuring element for you. Knowing the term matters mostly when you're reading the engines reference or troubleshooting an unexpected result and need to articulate that the structuring element shape didn't match the structures I was trying to find.