First – what is Zimbra? According to their website,
Zimbra is open source server and client software for messaging and collaboration – email, group calendaring, contacts, and web document management and authoring.
Simply put, it is a "MS Exchange for Linux"-type of an application without the associated licensing costs of MS Exchange, of course!
falko Timme of Howtoforge provides a 3-paged install guide on installing Zimbra on Ubuntu.
Just a word of warning, though. Zimbra has two versions – open source, which we are all familiar with and the commercial version, which costs money. Check out the differences and see where your organization falls in.