About the Geoprocessing task
With the Geoprocessing task, you can make use of services that run ArcGIS geoprocessing jobs on the server and send the results back to the client application. The Geoprocessing task requires an ArcGIS Server geoprocessing service, which you add as a Supporting Service. Geoprocessing services are based on models and can be published from either a toolbox or a map document containing a tool layer. See the ArcGIS Server Help book Geoprocessing services for more information on how to create a geoprocessing service.
The Geoprocessing task gives you access to much of the functionality of ArcGIS without having to add custom code to your Web application. For example, you can use the Geoprocessing task to access network analysis tools, select features, run geostatistical analysis models, and so on, without needing to learn ArcObjects or Web programming. You just create the model in ArcGIS Desktop, publish a geoprocessing service, and use the service in the Geoprocessing task. The Geoprocessing services book mentioned above contains many examples of functionality you could expose through geoprocessing services and tasks.