First off, fix your indentation, it's all over the place.

Code:
#include <stdio.h>
#include <stdlib.h>

int askFirstQuestion(int a)
{
  return (a >= 1 && a <= 7);
}

int main()
{
  int a;
  printf("1) Please enter your birthday between 1 and 7(example Mon=1, Tue=2..):");
  scanf("%d", &a);
  if (a >= 1 && a <= 7) {
    printf("%d\n", a);
  } else {
    while (!(askFirstQuestion(a))) {
      printf("%d\nPlease enter an appropriate day!\n", a);
      scanf("%d", &a);
      if (askFirstQuestion(a)) {
        printf("%d\n", a);
      }
    }
    return 0;
  }
}
Most of the code you have in main should be inside the function.
It should be the one to print the prompt, get an answer and loop until the answer is within range.

So your main should be
Code:
int main( ) {
  int birth_day = askFirstQuestion();
}