The geometry service helps applications do geometric calculations such as buffering, simplifying, calculating areas and lengths, and projecting. The geometry service provides an alternative to doing these calculations using fine-grained ArcObjects or a geoprocessing service. The geometry service is especially appropriate for applications built with the ArcGIS REST or JavaScript APIs.
More Information:
GeometryServer: http://cloud.insideidaho.org/ArcGIS/rest/Services/Geometry/GeometryServer