Groups are simply a group of members with special Permissions. With groups you get your "Staff Members" more organized. Staff Members can be more organized by not having to add each member as a Mod in every forum, you can just add the member to that group and they have the same permissions.
I also recommend you not only make a group called Site Staff, also make a group of "Promoters", which can appeal to the members if you make them Mod of 1 of the Default Forums like the Introduccion Lounge or something else, this way members can see that is they promote your site they wil be rewarded.
You also should take advantage of the topic of your site, if your site is a GFX (Graphics) site maybe make a group of Designers, which can take care of the graphic request. If you have a support forum, if its a computer support forum, make a group called "Hardware Support Team" or something along those lines.
Groups just make your forum look more sleek and clean. You can play around with your groups, it all depends on the topic of your forum and the tittle.
If you want to learn how to make your group read This Article third paragraph :)