Being able to save data to the cloud allows you to provide apps that can share data. Facebook, Twitter, Snapchat all rely on the cloud – what you post other users can access. There are a wide variety of ways to do this.
MBaaS stands for Mobile Backend as a Service. Instead of spending time creating your own server and writing the code to store and access data you can use a service such as parse that make it easier to do. This allows you to focus on making your app.