Why broken links matter
A link to a dead page is a dead end for the reader and a small signal that the content is not maintained. On pages you want to rank, keep outbound links working and pointing to the best current source.
Broken link building
Run the checker on sites in your niche. When a respected page links to something that no longer exists, you can offer your own page as a replacement: it helps the site owner and earns you a relevant link.