You can configuring your mobile device to connect to Zimbra.  We provide instructions for iphone and andriod devices.  Although Zimbra supports IMAP and POP, we recommend using ActiveSync for mobile integration.  ActiveSync (aka Microsoft Exchange) support is native to Apple IOS and Google Adnroid devices and provides consistent and continous connectivity between your device and your Zimbra server.

Please review the additional knowlegebase articles for more information.

To connect using Microsoft Exchange:
How to connect your iPhone to Zimbra using Microsoft Exchange (ActiveSync)

If you still want to use IMAP, use these instructions:
How to connect your iPhone to Zimbra using IMAP