What exactly is OWIN and what problems does it solve?

OWIN is a specification on how web servers and web applications should be built in order to decouple them and allow movement of ASP.NET applications to environments which were not supported before.

Prior to OWIN, when building ASP.NET application, you were inherently bound to IIS due to the heavy dependency on System.Web assembly.

OWIN itself does not have any tools, libraries or anything else. It is just a specification.