Web-Service
A web service is any piece of software that makes itself available over the internet and uses a standardized XML messaging system.
Simply a web service is a SaaS over web, authorized users / applications can access it utilize the functionality provided by the web-service
Mainly web-service is of two types
one is providing (producing) service over web.
Second one is accessing (Consuming) services provided by other / third party.
Using web-service we can do CRUD operations and can perform specific functionalities like Currency Conversion Rates... etc.
Here I'm going to give you a quick tour to implement Web-service using Salesforce.
You can find more about how to consume / produce web-service on Salesforce tab.