From http://www.w3schools.com (Copyright Refsnes Data)
A few years ago Web services were not fast enough to be interesting.
Thanks to the major IT development the last few years, most people and companies have broadband connection and use the web more and more.
When all major platforms could access the Web using Web browsers, different platforms could interact. For these platforms to work together, Web applications were developed.
Web-applications are simple applications run on the web. These are built around the Web browser standards and can mostly be used by any browser on any platform.
Using Web services, your application can publish its function or message to the rest of the world.
Web services use XML to code and to decode data, and SOAP to transport it (using open protocols).
With Web services, your accounting department's Win 2k server's billing system can connect with your IT supplier's UNIX server.
Reusable application components.
There are things applications need very often. So why make these over and over again?
Web services can offer applications components like currency conversion, weather reports, or even language translation as services.
Ideally, there will be only one type of each application component, and anyone can use it in their application.
Connect existing software.
Web services help to solve the interoperability problem by giving different applications a way to link their data.
With Web services you can exchange data between different applications and different platforms.
From http://www.w3schools.com (Copyright Refsnes Data)