The period p of a pseudorandom generator is determined by the interval at which a pseudorandom number in the generated output sequence X[i] is repeated for the first time, so that it is for every i: X[i] = X[i+p].
The period is dependent on the skilful choice of parameters for the generator, as only with a suitable choice of parameters the generator achieves the biggest possible period.
Once the periodicity is known, the random number generator is cracked, as for every pseudorandom number X[i] the next number X[i+1] is known. Good pseudorandom number generators therefore have very large period lengths where in practice it is not possible to save all the sequence members of the period.