Waitlisting is what happens when a UC Davis student signs up for classes on SISWEB, only to find out that they are full and you are on the waitlist. You have 12 days, starting from the first day of class to get into the class, either by someone else dropping out of the class, or by petitioning the Professor, T.A., or Department. If you are still waitlisted after the 12 days are up and do nothing, then you will be dropped from the course.
Usually if you are #1 or #2 on the waitlist, the professors may advise you to be patient because you will probably get into the class. However, the amount of time it takes and frequency of being waitlisted depends on the student's habits and willingness to wait for an opening, and while it varies from class to class, #3 on the WL and below often have a tougher time getting in. On the first day of the quarter, many students go up to the professor after class and ask about waitlist policy and their odds of getting in. Being on the waitlist can be stressful, but if you work hard during in the beginning or you are at the top of the waitlist, your odds are pretty good. But, it is very important to ask the professor at the start of the class, so you do not end up wasting your time and lose a chance to enroll in another course.