where we can use webservices and its related api's

That's a big subject that I'm not sure can be adequately addressed in a forum like this. To make it as succinct as possible off the top of my head: "to allow processes running on separate machines to connect to one another over a network, irrespective of their (possibly differing) operating systems, implementation languages and other hardware and software characteristics they may have (and which may change over time)".

You may wish to search for "what are web services" or some such phrase to find introductory articles that explain them in more detail.

Web Services is useful in integration of any application. By using web services, application can publish it functionality to rest of the world.
An application can be integrate with other application with using this application exposed web service methods, without knowing designing and implementation of
this application

For more you can Google this.