The map service is the way that you make maps available over the internet or your intranet. You'll make the map in either ArcMap or ArcGIS Pro, then publish the map as a service to your ArcGIS Server site. Map services can be added to web applications, ArcGIS Desktop, ArcGIS Online, and other client applications as a map image layer or a feature layer.
What can a map service do?
A map service makes maps, features, and attribute data available inside many types of client applications and can expose different levels of capabilities. When a map service is hosted on an ArcGIS Server site, it exposes additional functionality, such as dynamic drawing, query, and search. With ArcGIS Server, further web services may be available through the map service root URL that allow network analysis, vector feature editing, and so forth. One common use of a map service is to show business data on top of basemap tiles from ArcGIS Online, Bing Maps, or Google Maps. Many other ways to use a map service are described in Common reasons for using map services.
How do I start creating a map service?
When you've created a map in ArcMap and are ready to share it with others, choose File > Share As > Service > Publish Service from the main menu. The items on the Share as Service dialog box can help you get started sharing your map as a service. See Publish a map service from ArcMap for full instructions.
When you've created a map in ArcGIS Pro and are ready to share it with others, right-click the ArcGIS Server that you'll publish to in the Catalog pane, and choose Publish > Map Service. The items on the Select Map dialog box can help you get started sharing your map as a service. See Publish a service for full instructions.