With the use of API you can use their service on your site. Such as Google maps, login with google account etc. You can use api to improve user experience on your site.
It is an interface that queries the Google database to help programmers in the development of their applications.You can use it service on your site.
"Application Programmable Interface" Google’s API could be of some help for you, depending on your general level of knowledge or expertise in Web technology and your programming skills. Google API’s consist basically of specialized Web services and programs and specialized scripts that enable Internet application developers to better find and process information on the Web. In essence, Google APIs can be used as an added resource in their applications.
Adding a google +1 to your site is an example of using Google's API. their api is far more complex than just that, but if you are not a programmer, you wont use much of it