Why do people say there is modulo bias when using a random number generator?

Question

I have seen this question asked a lot but never seen a true concrete answer to it. So I am going to post one here which will hopefully help people understand why exactly the

Answer 1

Keep selecting a random is a good way to remove the bias.

Update

We could make the code fast if we search for an x in range divisible by n.

// Assumptions
// rand() in [0, RAND_MAX]
// n in (0, RAND_MAX]

int x; 

// Keep searching for an x in a range divisible by n 
do {
    x = rand();
} while (x >= RAND_MAX - (RAND_MAX % n)) 

x %= n;

The above loop should be very fast, say 1 iteration on average.