what is the usage of extern in c

1#include <stdio.h>
2extern int x = 32;
3int b = 8;
4int main() {
5   auto int a = 28;
6   extern int b;
7   printf("The value of auto variable : %d\n", a);
8   printf("The value of extern variables x and b : %d,%d\n",x,b);
9   x = 15;
10   printf("The value of modified extern variable x : %d\n",x);
11   return 0;
12}

1extern "C"{
2   int printf(const char *format,...);
3}
4main() {
5   printf("Hello World");
6}