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The extern keyword in C/C++ is short for external linkage

External linkage is the process of having the linker resolve references after compilation which allows functions and variables to be shared between translation units

main.c
// function is declared but not defined. Even when making use of external linkage, the function declaration is required in every translation unit that wishes to use the function / variable

int sum(int a , int b);

int main(void)
{
printf("%i\n" , sum(10 , 20));
}

math.c
int sum(int a , int b)
{
return a + b;
}

The linker will compare the function declaration in main.c with the definition in math.c. If they have same function prototype, the linker will link them together.

Functions by default have external linkage available to them without explicit use of the extern keyword. But variables need to be flagged as extern during declaration to make external linkage available.

Here is how external linkage can be used for variable using the extern keyword.

pi.c
float pi = 3.1415f;

main.c
extern float pi;

int main(void)
{
printf("%i\n" , pi);
printf("%f\n" , circle_area(1.0f));
}

pi can now be shared between multiple translation units now.

area.c
extern float pi;

float cicle_area(float radius)
{ return radius*radius * pi; }