Facets are the checkboxes, dropdown menus, fields and other UI elements often presented with a set of search results so the user can further sharpen and refine their query.
So a set of search results for “mens shirts” will show checkboxes for brands, dropdown for average customer review, and fields for ideal price range. Or a set of search results for “electric engine schematics” will show checkboxes for file formats, a dropdown for product line, and dropdown menus for document type, author, language, or date range.
Those menus and checkboxes that users are using to refine their search are facets.