Synching your Zotero is highly recommended! It will help back up your library and will allow you to use the same Zotero library across multiple computers and use group libraries with other Zotero users. Zotero can store your library and annotations on the cloud and use that to update other devices.
First, set up a (free, of course) Zotero.org user account. Then:
Repeat this configuration on each of your devices. Any updates you make on one of your computers will be reflected on the others.
For more details and help troubleshooting sync problems, check the Zotero site.