Unlike most academic journals, student-run law reviews generally permit authors to submit their scholarly articles to many journals at once. When a journal decides to accept a particular paper, the journal typically gives the paper's author a window of time in which to decide whether to accept the offer. It's understood that authors use this window to try to "shop up" the article, requesting an expedited review from more desirable journals (more desirable for whatever reason — higher prestige, a particular school, etc.). Those more desirable journals then give the article a quick read and decide if they want to move quickly and give an offer before the expedite window at the other journal closes.
This system may sound really odd at first, but it's not a terrible way of dealing with a world in which there are hundreds of journals looking to publish the most desirable articles possible and thousands of authors hoping to be published in the most desirable journal. Requiring exclusive submissions works well in fields with a handful of journals, but it's a lot harder in a field with hundreds of journals. (Can you imagine how many years it might take to run through journals until you finally get your offer from the Delaware State Journal of Labor &Employment Law?) Also, a grand "matching" system would take too much time: It may or may not be easy for authors to rank their preferences of journals, but clearly it would take an impossible amount of time for every journal to rank every submission.
In contrast, the traditional way law reviews work creates some sort of a market in scholarly works and yet is still relatively manageable. Journals that are the first to make an offer for a piece generally have an advantage in getting it (for a bunch of complicated reasons). On the other hand, authors have some limited assurance that their articles will have a chance to be considered at journals "up the food chain" during the expedite window.