In some businesses, IT wants nothing to do with installing and running an app. Under the SaaS model, since the software is hosted by the software provider, they take on the responsibility for maintaining the software and upgrading it, ensuring that it is reliable and meeting agreed-upon service level agreements, and keeping the application and its data secure. This eliminates the need to have very expensive IT expertise.
SaaS companies typically offer seamless, automatic, and very frequent upgrades as part of the ongoing subscription charge. Beceause these upgrades happen frequently and more incrementally than on-premise solutions, they typically also have significantly reduced testing and training costs.
While some IT people worry about security outside of the enterprise walls, the likely truth is that the vendor has a much higher level of security than the enterprise itself would provide. Many will have redundant instances in very secure data centers in multiple geographies. Also, the data is being automatically backed up by the vendor, providing additional security and peace of mind. Because of the data center hosting, you're getting the added benefit of at least some disaster recovery. Lastly, the vendor manages these issues as part of their core competencies—let them. Save your IT staff time for work on the systems they know best.