Building cross-platform applications in Xamarin Studio, you often need to be working on one single platform at a given moment.
Since Xamarin Studio allows having both iOS and Android projects under the same solution, when building or deploying, they all get compiled. This is not very efficient, since you only want to deploy one platform at a time, either iOS or Android.
The solution configuration specifies how projects in that solution are to be built and deployed. A solution can have multiple configuration mappings specified (build configuration, release configuration etc), each containing a combination of a configuration and a platform.