iid(zero, sigma square) means that the variables are identically and independently distributed with mean zero and variance sigma square. Sigma square is the variance of the distribution.
As the family of random variables is called "iid", then sigma square applies to any member of this family, independently of others. In other words: the covariance matrix of this family is diagonal, with all diagonal entries being identical and off-diagonal terms equal exactly to zero.
This sigma square refers variance of the population which is assumed to be modeled by a distribution F and n (sample size) random variables are assumed to be independently and identically distributed (iid) as the distribution F.