it lets you shift the costs of data storage, management, back up, disaster recovery, and server provisioning to a third party. The theory is that by specializing in these operations and by providing them for multiple customers, the third party can use the advantages of volume to provide these services to you at a lower price than you currently pay to do them yourself.
The downsides are that you’re dependent on an external Internet connection; that question of the security of your data in someone else’s hands (including the legal issues, depend on what the data is); the long-term viability of the third party; and all the other issues when you outsource a critical part of your company’s infrastructure.