A random seed (or seed state, or just seed) is a number (or vector) used to initialize a pseudorandom number generator.
For a seed to be used in a pseudorandom number generator, it does not need to be random. Because of the nature of number generating algorithms, so long as the original seed is ignored, the rest of the values that the algorithm generates will follow probability distribution in a pseudorandom manner.
-- wikipedia
So, random function could be implemented like this:
int rand_r(unsigned int *seed)
{
*seed = *seed * 1103515245 + 12345;
return (*seed % ((unsigned int)RAND_MAX + 1));
}
(sample taken from glibc)