It's something you setup in MySQL so that it stores the changes in a log. See the mysql manual on how to do this.
If these logs are stored in place where laravel can get to them then you should be able to push them onto your remote server. Then you can run some queue job on the remote machine to sync the machine.
This is highly experimental and nothing I've ever tried doing so it might not be possible.
This will only transfer changes done after you started logging so the old data needs to be exported with mysqldump and imported so you have the data in sync.