It appears to me that even if I refer to a function in another file with out extern declaration, gcc can still compile that unit. So I am wondering whether the extern declar
As far as I remember the standard, all function declarations are considered as "extern" by default, so there is no need to specify it explicitly. That doesn't make this keyword useless since it can also be used with variables (and it that case - it's the only solution to solve linkage problems). But with the functions - yes, it's optional.
A little more verbose answer is that it allows you to use variables compiled in another source code file, but doesn't reserve memory for the variable. So, to utilise extern, you have to have a source code file or a library unit that contains memory space for the variable on the top level (not within functions). Now, you can refer to that variable by defining an extern variable of the same name in your other source code files.
In general, the use of extern definition should be avoided. They lead easily to unmanagable code and errors that hard to locate. Of course, there are examples where other solutions would be impractical, but they are rare. For example, stdin and stdout are macros that are mapped to an extern array variable of type FILE* in stdin.h; memory space for this array is in a standard C-library unit.