Web API is a feature of ASP.NET MVC 4. It is an API for writing REST web services. One might ask why we need another API. After all, we already have WCF Rest Service a few years ago. It is also fairly easy to return JSON from an ASP.NET MVC controller using JsonResult. For a long answer, it is best read ScottGu;s blog or the WCF site. The short answer is that Microsoft want a way to make it extremely easy to create REST services and to provide lots of features. ASP.NET MVC is the best place. Currently, the .Net REST/Json story is fragmented and there are several Json serializers in .Net. ASP.NET Web API represents the future, consolidated API for this feature.
It is fairly easy to get started with ASP.NET Web API. For those who likes to watch video, Jon Galloway’s 6 short videos provides a very quick start and it takes only 24 minutes to watch them all. For those who like read and type, the ASP.NET site has 7 short chapters that can be read in an hour or two. Many bloggers are blogging the Web API. I would recommend Stephen Walter’s blog for a quick introduction. Finally, I strongly recommend looking into some of the samples.