Steffan's answer hits the core points, and there are some additional benefits to using a backend-as-a-service (BaaS) platform beyond simply having the infrastructure / DevOps side of things handled for you. (Full disclosure: I am an engineer at Kinvey, a backend-as-a-service provider).
Many of these services provide RESTful APIs to access your data directly. Rather than spending time to roll your own (and reinvent the wheel yet again), you typically get your own data API baked in and ready to go.
BaaS providers typically offer code libraries to simplify connecting to your API.
It's often more than just application data. For example, at Kinvey, we provide large file (blob) storage as well. If you have any images, videos, etc, you can store them with zero setup.
Some providers also offer analytics on your API usage - another wheel that you don't need to reinvent
Partnerships with other providers: for example, Kinvey provides push notifications via Urban Airship
All together, it probably makes sense to take a look at BaaS to see if it can fit your needs.