Some development environments (IDE's) for Linux have that kind of thing. It's a pane with all of the functions listed.
www.freshmeat.net and search for C or C++ IDE. They work only under a given windowing environment, e.g. gnome, kde....
Also UltraEdit, which runs under Windows, will show a window that lists all of the functions in a given C file. You can download a demo version, and use it to look at the source file(s) you want to check.
www.ultredit.com
I think what those folks are talking about is nm. nm lists all of the symbols in a compiled C binary, if it has not been stripped. It also lists all of the external entry points, all of the global variables. I have never seen one that does this for C source.
They may also mean ctags - this creates an index file of functions. The somewhat human readable file is usually just called tags. Maybe you can use that. The first "column" is a list of functions, and you can write some perl or sed to extract the names.