Standards are important; that's why we have so many of them. The latest version of the .NET Standard is version 2, and .NET Core 2 implements this. A good way to think about .NET Standard is it's an interface that a class would implement. The interface will define an abstract API, but the concrete implementation of this API will be left to the classes that inherit from it. Another way to think about this is like the HTML5 standard that is supported by different web browsers.
Version 2 of the .NET Standard was defined by looking at the intersection of the .NET Framework and Mono. This standard was then implemented by .NET Core 2, which is why it contains more APIs than version 1. Version 4.6.1 of the .NET Framework also implements .NET Standard 2, and there is work to support the latest versions of the .NET Framework, UWP, and Xamarin (including Xamarin.Forms).
There is also the new XAML Standard that aims to find a common ground between Xamarin.Forms and UWP. Hopefully, it will include Windows Presentation Foundation (WPF) in future. As this is a book about web applications, we won't go into XAML and native user interfaces.
If you create libraries and packages that use these standards, then they will work on all the platforms that support them. As a developer who simply consumes libraries, you don't need to worry about these standards. It just means that you are more likely to be able to use the packages that you want on the platforms you are working with.