What is web service who writes it and how it works?

Answer 1

1. A web service is a service that is available for use over the internet. "Servers" are called such because they provide "services." Don't be confused by someone pointing at a computer and calling it a "server", strictly speaking this is incorrect even though it is a vernacular used nearly everywhere. What the person means is that computer runs server software that provides services over a network.
2. As for who writes it, there is no definitive answer other than "the programmer/s". As there are far too many web services and programmers of them out there to discuss.
3. Similarly for how it works, it depends on the specific service you want to discuss and since there isn't one named there are too many out there to mention.