The simplest definition of a Web service is an application that provides a Web API. The Web API exposes the functionality of the application to other applications. The Web API relies on Web services technology to manage communications. Web services technology is pervasive, vendor-independent, language-neutral, and very low-cost.
The purpose of a Web API is to enable application integration. More specifically, a Web API lets you integrate heterogeneous applications. You can use Web services to achieve many different goals. You can use them to implement internal point-to-point application integration projects. You can use them to consolidate your development efforts and reduce redundant applications. You can use them to implement a general-purpose integration bus for your internal application systems. And you can use them to make it easier for your partners and your customers to do business with you.
Web services do not represent a new business model. Instead Web services are a technology that you can use to build systems to support a business model.
IT departments are being asked to do more with less. There's less money in the budget to buy software, and there are fewer people to do the work. Nearly every application development project involves some level of application integration. It just makes sense to reduce the cost and simplify the process of doing integration. Web services are an obvious choice.