Visual Studio App Center is a service provided by Microsoft that offers a comprehensive mobile DevOps toolchain. One of the biggest barriers to entry when it comes to setting up the DevOps tooling is the amount of configuration, integration, and maintenance that is involved. In my experience, setting up DevOps tools means integrating several services, writing tons of scripts, and typically dedicating a developer to maintaining the build server. App Center offers a streamlined solution that minimizes configuration and pretty much eliminates integration and maintenance since it is a centralized and hosted service.
All of the components of App Center can be accessed via the App Center website or API. The monitoring components also require the App Center SDK to be included in your mobile app package. For Xamarin apps, the SDK is available via NuGet.