It is a Roslyn based interpreter that lets you do REPL based programming in C# similar to other REPL languages. CSX files are used with csi.exe which is the interactive C# REPL. There is a window in Visual Studio called "C# Interactive" that lets you run this as well. If you want to interactively program with a REPL, use csx files. OR if you want to make quick snippets to interact with both your Visual Studio and as a command line.
https://msdn.microsoft.com/en-us/magazine/mt614271.aspx
https://www.red-gate.com/simple-talk/dotnet/net-development/going-interactive-c/
In the .NET world, lots of people still use
LINQPad to do ad-hoc exploration and execution in .NET languages. But this was because there was no REPL to do quick, ad-hoc programming. However LINQPad is God-like when you are exploring data interactively.
CSX files are not a replacement for Powershell or a replacement for the old Windows Scripting Host(VBScript or JScript)