.NET Core is a free and open-source managed software framework for Windows, macOS and Linux.
It is completely overwritten .NET framework. .NET Core is independent on original .NET framework version and both .NET and .NET Core frameworks will be developed and actively maintained in the future.
.NET Core is not replacement for .NET Framework, but it is likely that developers will start building most of the new projects on .NET Core.
It consists of CoreCLR, a complete runtime implementation of CLR, the virtual machine that manages the execution of .NET programs.