A web service is generally defined as an interoperable machine-to-machine communication over the wire (network). In the context of cross-platform application, the most important term in this definition would be "interoperable". Web services written in different frameworks or languages and running on different type of runtimes and hardware conform to the same standards, most of which can be consumed by applications running on a variety of platforms, including Xamarin target platforms.
Xamarin target platforms, namely iOS and Android, and Windows Runtime, can access stateless web services using the TCP/IP (short for Transmission Control Protocol / Internet Protocol) stack over a secure or non-secure HTTP (short for Hypertext Transfer Protocol) transport layer. Even though various data representations can be consumed via web services, JSON and XML are the most common text-based notations used.