SQL requires the "FOR UPDATE OF" clause when declaring a cursor that will be used to update rows. This specifies which columns can be updated through the cursor and is necessary for positioned updates using UPDATE...WHERE CURRENT OF.
The FOR UPDATE OF clause on a SELECT/cursor declaration tells the database that specific fields will be modified, letting it lock the appropriate rows/columns for the update. The other phrasings ("With Update", "Updating", "To Update") aren't valid clause syntax in this context.