Normally a breaking change means after you apply the change it's not easy/straightforward to rollback to the older version if you want to do that for whatever reason.

For example, a new version is released and underlying database table or structure changes. You upgrade properly, and find the new version has some bugs (or you simply don't like it). If you want to use the older version again until the newer one is fixed it's not a matter of simply point to old version.

As the database structure has fundamentally changed underneath in the new version, when you put back the old version it simply doesn't understand the new structure and might stop working. You need ways to be able to make the DB structure compatible with the older application.

If the application is stable the devs might provide ways to do this. But since this is an alpha... You're on your own.

TL;DR it means the older and newer version of the application aren't strictly compatible with each other