Why the background color might not print by default
Word treats background colors and images as a screen-only decoration by default, on the assumption that most documents printed on a home or office printer do not need a colored background. The "Print background colors and images" option in Display settings has to be turned on explicitly to override that.
Where this is most useful
Invitations, flyers, and announcements meant to be viewed on screen or as a PDF benefit the most from a page color, since it replaces the plain white default without needing a separate design program.
Frequently Asked Questions
Does a colored background affect the file size much?
A solid color adds almost nothing to file size, but a photo or textured fill effect used as a background can noticeably increase it, especially across a long document.
Will the background color show up if I export the document to PDF?
Yes, exporting to PDF preserves the page color or fill effect regardless of the "print background" printer setting, since PDF export renders the page as designed rather than going through the printer driver.