Zotero can store a copy of your library on the Zotero.org server. This is useful for several reasons: it provides a backup, lets you access your library on the web from anywhere, and keeps your library up to date if you install Zotero on multiple computers.
First, you’ll need to set up a Zotero user account. Then:
Repeat this configuration on each of your computers. Any updates you make on one of your computers will be reflected on the others. This even works to synchronize your library among Windows, Mac and Linux computers.
For more details and help troubleshooting sync problems, check the Zotero site's file syncing support page.