The term web service is either

(generic) a service offered by an electronic device to another electronic device, communicating with each other via the World Wide Web, or
(specific) a web service implemented in the particular technology or brand, eg W3C Web Services.In a web service, the Web technology such as HTTP—originally designed for human-to-machine communication—is utilized for machine-to-machine communication, more specifically for transferring machine-readable file formats such as XML and JSON.
In practice, a web service commonly provides an object-oriented web-based interface to a database server, utilized for example by another web server, or by a mobile app, that provides a user interface to the end user. Many organizations that provide data in formatted HTML pages will also provide that data on their server as XML or JSON, often through a web service to allow syndication, for example Wikipedia's Export. Another application offered to the end user may be a mashup, where a web server consumes several web services at different machines, and compiles the content into one user interface.