Extensions add media-specific fields to sitemap entries. They matter most where the media is loaded by script or served from another domain, because in those cases page-level discovery is unreliable.
Image extension
Lists image URLs associated with a page. Useful for galleries, lazy-loaded images and CDN-hosted media.
Video extension
Carries title, description, thumbnail, duration and player location. Google uses these for video results, and several fields are required rather than optional.
News extension
Only for sites in Google News, and only for articles from the last two days. Older entries should be removed.
Alien Road recommends: use the image extension whenever your images live on a separate CDN domain. It is the one case where we consistently see a measurable difference in Google Images coverage, because the page-level association is otherwise ambiguous.