extern is needed because it declares that the symbol exists and is of a certain type, and does not allocate storage for it.
If you do:
int foo;
In a header file that is shared between several source files, you will get a linker error because each source would have its own copy of foo created and the linker will be unable to resolve the symbol.
Instead, if you have:
extern int foo;
In the header, it would declare a symbol that is defined elsewhere in each source file.
One (and only one) source file would contain
int foo;
which creates a single instance of foo for the linker to resolve.