What is the difference between ASP.NET MVC 6 and ASP.NET Core 1.0 and the reason behind the core framework?

MVC 6 was part of ASP.NET 5, but due to some major changes in the code base, they decided to change its name from ASP.NET 5 to ASP.NET Core.

You can read about here: http://www.hanselman.com/blog/ASPNET5IsDeadIntroducingASPNETCore10AndNETCore10.aspx