By email, you may have received calendar invites and your mail just shows them as .ics attachments. The Zimbra calendar usually does not recognize these formats.
In this case:
1) Save the .ics attachment locally.
2) From within the Zimbra Web Client, select PREFERENCES, and then the CALENDAR tab.
3) Click the IMPORT heading, browse your file system to locate your .ics file and then click the IMPORT button.
4) In the resulting popup window, either select an existing calendar or create a new one to import the ICS events into.