This is a fairness requirement.

If other processes are trying to access the critical resource when a new process also tries, there should be a guaranteed bound on the number of times these other processes are allowed to access the resource before the new process gains access.

If there is no guarantee, then it is possible that some process may starve waiting for the critical resource.

Note that if no bound is guaranteed, starvation may or may not occur. But if a bound is guaranteed, then starvation will not occur.

(No good concrete example at this point.)