With ArcGIS Desktop, you can create geographic information that is captured and preserved as geodatabases, map documents, geoprocessing toolboxes, image files, and so on. Each of these can be published and shared as GIS web services using ArcGIS Server or ArcGIS Online. For a full list of services that are available, see What types of services can you publish?.
ArcGIS Desktop is designed to work with services. For example, when you click Add Data, you can browse to a server connection and add map and image web services into your table of contents, just like you would with any other data source.
Web services may be used in more subtle ways, too, such as when performing geocoding or network analysis operations. Be aware of places where you might take advantage of web services to get functionality or information beyond what is available on your local computer.