Can any one explain me what is REST API and SOAP API. Also the example scenarios where these can be used ?
SOAP API and REST API are two commonly used API's to expose your data from force.com platform to other platforms(JAVA ,.NET ,etc) or to allow external application to invoke Apex methods.
This is an interesting blog and may answer your question very well.
API described in Salesforce documentation above.
1)Supports data in the form of XML only 2)Requires WSDL for the integration 3)Use SOAP API in any language that supports Web services. 4)It is a standard protocol and needs more bandwidth and resources.
REST API 1)Supports both XML and JSON format 2)Preferred for mobile and web apps since JSON being Lighter the app runs smoother and faster 3)It is more of an architectural system and requires less bandwidth and resources.
You can also use Apex SOAP and REST Web services to expose data from platform or allow an external application to invoke Apex methods.
You may want to refer to the Apex guide to learn more about this.
Another thing I would add to Mohith's response is that since both REST and OAuth rely strongly on HTTP/S standards - it makes it very easy to find existing libraries to communicate with the API's for nearly any language. Even with there is no "Force.com toolkit", many languages know how to at least speak HTTP, if not REST/OAUTH/JSON.