OWIN is a specification that decouples web applications from web servers by establishing an abstraction layer, allowing applications to run on any OWIN-compliant server. Katana is a set of components built by Microsoft using OWIN specifications, including Web API, ASP.NET Identity, and SignalR. In a Katana application, requests flow through layers - the application, middleware components, the server, and the host process manager. This allows flexibility in choosing and arranging middleware before requests reach the server.