As far as I know, browsing path is where the debugger should look for files when breaking/stepping into source files thats not in the library path.
Lets say that you have a thirdparty component that you use. You point the library path to the directory where the pre-compiled dcu-files of that component are. Your project will use these dcu-files when you compile. This is good, because it wont be recompiled every time you do a build.
But by including the compiled dcu files, you loose the possibility to debug the thirparty component. If you include the path to where the source files are in the browse path, the debugger will find the source, and allow you to step in to it.
The default settings for the vcl show this. In library path they have put $(BSD)\Lib, and in the browsing path they have put $(BDS)\SOURCE\WIN32...
Update: There are two different kind of search paths: Compiler search path and debugger search path. The first is there the compiler looks for files during compiling, and the second is where the debugger looks for source files during debugging.
The compiler will only find files in the Library path or the projects search path.
The debugger will find identifiers in the compilers search path plus the browsing path, the debug source path for the project, and the global debug search path.
There should not be any difference in specifying things globally or pr project.
Best Answer
Make sure that the path is already present in the compiler search path (not resource compiler!) for the project or the library path of the IDE.