Similar to other Firefox extensions (and other software in general), Zotero checks periodically for updates from the Center for History and New Media servers. In particular, we are constantly adding support for new catalogs and sites, and we push these changes out to current users once a day. In no way is Zotero reporting on what you’re doing, looking at, etc. We’re just upgrading the software to support more sites.
Zotero also sends an error report if a site translator fails to save from a web page. This lets us quickly diagnose and fix problems and ensure continued functionality for users.
Translator update checks and error reports can both be disabled from the Zotero preferences. Update checks for Firefox add-ons in general (which, in Zotero's case, will contact either zotero.org or addons.mozilla.org, depending on where you downloaded Zotero from) can be disabled from the Firefox preferences.