Why do we need web-services? How different is it from normal web-applications?

There are many advantages of using webservices. The main advantages over a regular http application is that it uses SOAP messaging wich is much more efficient and less bandwidth costly.

Another advantage is that Service Transport, XML Messaging, Service Description and Service Discovery layers use a standard protocol witch make it easy for developers to develop functionality irrespective of programming languages.

Suppose you are a provider of a service, say weather forecast. Why make developers, go to your website, scrab your page and then extract the data that they need? Wouldn't be easier to develop this services that a developer can pass in a date and get back a well defined xml document containing all the info they need? The same happens for all type of cases...

http://www.w3schools.com/webservices/ws_intro.asp

What are Web Services and why use them?

A web service is a software system designed to support interoperable
 machine-to-machine interaction over a network. The basic web services 
 platform is XML + HTTP(S).XML provides a language which can be used 
 between different platforms and programming languages 
 and still express complex messages and functions. HTTP 
 (or its secure form HTTPS) is the most widely 
 used Internet protocol. In combination they help to create an interface
 that communicates using openly defined, standardized protocols, 
 are self-contained and self-describing,and can be discovered and 
 used by other applications. Web services can help to solve interoperability
 challenges by giving your applications a way to integrate their data and 
 business processes with OpenClinica.

more deatails...

https://docs.openclinica.com/3.1/technical-documents/openclinica-web-services-guide/what-are-web-services-and-why-use-them#content-title-3006