What does "Application review begins ..." practically mean in job ads in computer science in USA?
It means that, shortly after date Y, the committee in charge of reviewing applicants will meet and discuss the applications that have been received up to that point and, if they like some of the candidates, they will be invited for interviews and, depending on how it goes, may get an offer. They committee may revisit the applicant pool at a later date and, if the position is still open, they may consider further applicants. So, in principle, you can apply whenever you want but if you wait until after date Y, you may miss out. Of course, it can happen that all good candidates are late but you shouldn't count on that.