The Category: drop-down is used to select the category from which the exported questions will be taken.
Some import formats (GIFT and XML Format) permit the category to be included in the writtenfile, enabling the categories to (optionally) be recreated on import. In order for this data to be included the Write category to file box must be ticked. If this is selected you can also embed the category context by ticking Write context to file. Deselect the context option for compatibility with older versions of Moodle.