Web API is a new Microsoft framework for building HTTP services and applications on the .NET platform. It aims to simplify and standardize the HTTP area, supporting both REST and RPC styles of services. Web API can be self-hosted without IIS or ASP.NET by using OWIN, and integrates concepts from WCF like content negotiation and message handlers with an MVC-inspired programming model using controllers and routing. The framework emphasizes building services around HTTP concepts like requests, responses, status codes, and headers in an asynchronous and extensible manner.