The most popular reason for using a third party email service is to help comanies reduce the burden on IT staff, according to this research from software development company Spiceworks. Other features, such as the ability to back-up and archive emails, and manage email boxes, also feature highly.
These days, though, its hard to think of a good reason why organisations would want to manage their own email. Aside from companies in the finance sector, or working in other sensitive areas, such as government on military, where there are security issues to consider, there is no good reason for managing email yourself. Its rather like generating your own electricity. Its possible to do, and may even be cost effective for some companies. But its an unnecessary distraction. Better just to focus on your core business.