It's called "core", because it doesn't contain the Windows desktop UI toolkits, like Windows Forms and Windows Presentation Foundation (WPF), and excludes some other Windows-specific functionality.
Additionally, this is the first version of .NET in which apps can be totally self-contained. Previously, you'd need to install the .NET Framework on your machine to run .NET apps. That is no longer a requirement in .NET Core 1.0.
So, it's a pretty huge release. And really the first time in decades that MS has built it's premier dev stack with multiple OS support.
[0]: https://github.com/dotnet/core/blob/master/release-notes/1.0...