A library is a file that contains executable code. In Windows, executable code is stored in either an EXE file, which is an executable program, or a DLL file, which is a dynamic link library. The only real difference between an EXE and a DLL is that an EXE has an entry point, i.e. a method that is executed first when the file is executed, which allows them to be run directly, whereas a DLL has to be used by an EXE or another DLL. In VS, when you create a new project, you can choose (amongst others) the Windows Forms Application template, which compiles to an EXE, the Windows Control Library template, which compiles to a DLL and is intended to be used by a Windows Forms application, or the Class Library template, which compiles to a DLL and can be used by any application. The term "library" is used in other languages besides .NET too, e.g. jQuery is a JavaScript library. In general, it simply means a file or files that contains types, members, functions, etc, that you can use in your application so that you don't have to write that code yourself over and over. It's just a chunk of reusable code to save you writing that code repeatedly.
If you are who I think you are then I believe I have already directed you to a number of links. What I believe you're looking for is not a library that extends the RichTextBox but a library that provides an object model for working with RTF text. You want something analogous to the HTML Agility Pack, which makes working with HTML easier but that doesn't mean that it extends the WebBrowser control. When I searched I specified .NET and I saw a number of options that were written in C#. C# is a completely different language to C, although C# syntax is based on C/C++ syntax. That's not a problem though. Almost the entire .NET Framework class library is written in C# and you have no issue using that. For instance, the RichTextBox control that you use is defined in the System.Windows.Forms.dll library and that was written in C#. Once compiled, C# and VB.NET code produces the same result and either language can use libraries written in either language. In fact, they can use libraries written in any .NET language, including F#, Delphi or others. A .NET library is a .NET library.