(Seth Wood, UVA Law '03, clerked at the 5th Circuit and works at a D.C. firm.)
Law Review serves completely different functions for different people at different times. I will try to hit on the major functions and why an average, everyday law student should invest (see also sink, donate, give over, throw away) a weekend and try out for the journal.
At the most mercenary level, LR acts as an easy proxy for intelligence. It is the A-B honor roll from high school. Most law schools do not give their students a class ranking and definitely do not list the best third or quarter of the student body for a given grading period. Consequently, for employers who want an easy means of separating out applicants, LR makes an easy first cut. Of course, failing to list LR on one's resume does not prevent one from getting a prestigious job or even a worthwhile clerkship. If a student has a good connection to a particular employer or judge, that student won't have to rely on LR so much.
For most potential employees, however, that LR acts as an easy way of comforting the employer - "I can either take law school tests well, or I can bluebook and write a quality journal tryout at least one weekend in my life!" More seriously, one might argue that those who actually make LR have some other traits (dedication, devotion, turning all the night time into the day) that would prove useful to a judge or a firm.
At the more highfalutin level, LR gives students a chance to interact with authentic Legal Scholarship and the law professors who write it! For most students who can't decide whether to try out for LR, this benefit likely won't push someone in one direction or another. Those who like legal scholarship will likely try out for LR. Even if they don't make it, they'll probably spend a great deal of time editing articles for a specialty journal at their school. In truth, those who work on pieces typically can become about as involved as they like. A senior Editor/ Leader person usually doesn't have enough time to dedicate 100% of her efforts to editing a piece. Consequently, that Leader splits up editing responsibilities amongst a number of new people. If you have a particular interest in the article, that Leader would probably love for you to take a crack at editing/ formatting/ whatever.
Okay, so LR can get someone a job and a shot at working with law geniuses. Is it fun? That completely depends on the people with whom you work. As a regular ed board member, a standard 2L position, you will have to perform fairly menial tasks and invest a fair amount of time. As a managing board member -- articles editor, EIC, etc. -- you likely would take charge of editing an entire piece, would assist in selecting articles for publication, etc. In essence, with great seniority comes great responsibility. If you choose to take on a managing board spot (admittedly, a lot of ed board folks are quite happy to remain on ed board through their third year), you will spend a great deal of time in the LR office.
If you enjoy spending copious amounts of time with the other people who have been selected to the Managing Board, you'll have a great time. If you are stuck with special people who actually discuss versions of the Bluebook in manner reminiscent of High Fidelity, it might not be as fun. Fortunately, I had the opportunity to work with a lot of very normal and fun people. LR generally and Managing Board in particular made my 3L year more enjoyable and more fulfilling. While some people ultimately might not like the experience, if someone has any inkling to try out the journal, that person should spend a weekend and see if the Review would fit their preferences.