Broken link building is the process of finding broken (dead, 404-ing) links on relevant, authoritative websites, then reaching out to the site owner to point out the issue and suggest your own relevant content as a replacement.
It works because it flips the usual outreach dynamic: instead of asking someone to add a link purely to benefit you, you're helping them fix something that's actively hurting their own site's user experience and credibility. That's why acceptance rates for genuine broken link building outreach tend to run well above generic link request outreach.