AYour instincts are in the right ballpark-the rehearsal dinner is a much, much more relaxed affair than the wedding. Yep, it should never outshine the big day. And here's the great part-within reason, it can sort of be whatever the hell your parents want. Let's say you have some ornate wedding with ice sculptures and the whole nine; in that case, a good 'ol fashion barbecue is a nice contrast. Or they could do something else ornate (without overshadowing) to fit in the theme. See how that works? You can spin this event in one of two ways: 1) fitting in a theme; or 2) appealing contrast. Either way you win.
So. It can be as freeform as you'd like. Three other major responsibilities, two direct and one indirect:
1) (Direct) Pay for it.
2) (Direct) Manage the guest list
3) (Indirect) Avoid conflict with the bride
The first is simple (and painful) enough: payment. Obviously this isn't set in stone. More and more modern couples are carving up the wedding expenses in a million different slices. Traditionally, though, your parents would foot the bill. (We're guessing that you know this or that you have some other financial arrangement already lined up.) The guest list - you and your fiancée will need to help them with this. How the hell is your mom going to know which of your friends to invite? The key, as with most of wedding planning, is to solicit input early from the key parties (the bride and the bride's family). You don't want any 11th hour surprises.
The third responsibility is the most important-staying out of the bride's warpath. From the tone of your email, it sounds like your parents aren't too hardcore or demanding or particular. This is good. You're probably in great shape. Be fortunate you don't have parents that have a very, very, veeerrrry precise idea of exactly how they want their rehearsal dinner. I would suggest that they go with the flow, ask you and the bride what type of event you want (formal or casual?) and not overcomplicate things.
Other minor responsibilities, of course, are to thank the guests at the dinner itself, give you both a toast, and avoid some type of Meet-the-Fockers showdown with your in-laws. Piece of cake. If there's anything else more specific you need just let us know.
Good luck and congratulations.
P.S. Have you seen our article on rehearsal dinners? Check it out here