.NET Standard is a specification defining APIs that all .NET implementations must provide, ensuring code compatibility across platforms. .NET Core is an implementation of the .NET Standard, optimized for cross-platform development and deployment.
Using .NET Standard libraries allows developers to write code once and share it among different applications targeting various platforms (e.g., Xamarin, UWP). When building cross-platform applications with .NET Core, developers can leverage these shared libraries, reducing code duplication and maintenance efforts.