Law review is a legal journal that is published and ran solely by law students. It's very competitive to get on law review, because as you can tell from my prior post only top students are invited on. If you aren't in the top ten percent, then you have to compete in a write-on competition and hope your writing skills are good enough to carry the day. I can tell you more about that if you want.
Anyway, the law review at USD publishes 4 issues a year of articles written by professors and students (very competitive to have your student work published). Check out USD's law review website under the publications section of the USD law website. Law review 2L members do all the citechecking of the articles, meaning they gather the sources, verify there is support for all the propositions, etc. 2L members are also required to write a student comment (at least 30 pages), which is a work of legal scholarship requiring lots of research. If the law review board finds a 2L's comment to be exceptional, it will publish it in the law review. Then in the spring of your second year, law review members may apply for law review board positions. These are actual editor positions - meaning you do substantive and technical edits on the articles. Very cool. I was both a law review member and board member -- loved it. Plus, you get course credit for doing law review (pass/fail so it cushions your GPA) and if you're on the board, you get a stipend (not a bad deal, but a lot of work).
Law review is very important for a couple reasons. First, during recruiting season, top law firms (what people call Big Law) almost without exception require law review membership before they'll even interview you. That's because, it's indicative of your class standing (for the most part). Second, law review is great from a practical stand point because it hones your writing and research skills, which will come in great handy when you work as a summer associate at a law firm after your second year and, of course, when you get into practice. In short, law review is a high honor.
We also have an international law journal at USD -- it's much less competitive to get on to that, but it's also much less prestigous. However, if you don't get onto law review, definitely do the international law journal because a journal is better than no journal.
Hope that helps.