What can break
Removing an API field, making an optional value mandatory, or changing sign-in rules can break existing software. Changes to screens or workflows can also disrupt people who rely on the old behaviour.
Coordinate the transition
Breaking changes can be necessary, for example to fix a security flaw. Teams can ease the transition by identifying affected users, explaining what must change, and giving advance notice. They may also run old and new versions in parallel.
Under semantic versioning, a new major version signals a breaking change to a library. It does not tell users how to update. Even undocumented behaviour matters if people reasonably rely on it.