As an ESRI user, you surely know how to publish some data in a map service. This lets you create a web service that can be used by a client who wants to show the map and data. This is the proprietary equivalent of exposing data through a WMS service.
With WMS, you can inquire the server for its capabilities with an HTTP request:
$ curl -XGET -H 'Accept: text/xml' 'http://localhost:8080/geoserver/wms?service=WMS&version=1.1.1&request=GetCapabilities' -o capabilitiesWMS.xml
Browsing through the XML document, you'll know which data is published and how this can be represented.
If you're using the proprietary way of exposing map services with ESRI, you can perform a similar query that starts from the root:
$ curl -XGET ...