.NET Core is a new version of .NET Framework. Today, it's common to have an application that runs across devices; a backend on the web server, admin front-end on windows desktop, web, and mobile apps for consumers. So, there is a need for a single framework that works everywhere. So, considering this, Microsoft created .NET Core. The main objective of .NET Core is to make .NET Framework open-source, cross-platform compatible that can be used in a wide variety of verticals, from the data center to touch-based devices.
There are some limitations with the .NET Framework. For example, it only runs on the Windows platform. Also, you need to use different .NET APIs for different Windows devices such as Windows Desktop, Windows Store, Windows Phone, and Web applications. In addition to this, the .NET Framework is a machine-wide framework. Any changes made to it affect all applications taking a dependency on it. Hence .NET Core was developed.