The sync feature to keep your library up to date between multiple computers running the same version of Zotero.
First, set up a (free, of course) Zotero.org user account. Then:
- Open Zotero preferences and select the Sync tab.
- Enter your Zotero user name and password.
- Check the "sync automatically" box.
- Check both boxes under File Syncing and choose Zotero storage for My Library. This will sync your PDF attachments as well as citations (more info).
For more details and help troubleshooting sync problems, check the Zotero site.