The four-month grace period plan is described on this website:
http://www.payroll.ucla.edu/ptr/f4leave.asp (scroll down to section F4.3)
The explanation on the web page is rather complicated, but it appears that UC employees accrue, or earn, their vacation time. (They earn X amount of vacation hours for every hour actually worked.) There is a maximum amount of vacation time that each employee can earn. If he earns that maximum amount and has not used it, he may lose it, unless he files a request for a four-month grace period.
For example, you've been working at the university for two years, and you haven't yet taken any vacation time because you're just too busy. You'll get a notice from Personnel telling you that you have accrued 280 hours of vacation time that you must use by May 1, or else those hours will be forfeited. If you simply can't get away by May 1, you can apply for an extension, or "grace period" of up to four months, asking to keep those earned vacation hours "on hold" to use at a later date.