Everyone else above me has pretty much well-explained what a 'mini-mod' is; someone who helps out in there own little section, and doesn't do much else. The end. Poof. You don't get that beautiful red-text or anything in the game, you just help at your assigned little section- like Feareh posted, the most typical places in which someone would get a section to look after and what not would be in the roleplaying boards, or like others said- preset contests and other kinds of contests.
But, from what I've heard there's also another 'definition' to this or whatever- this would be the 'alternate' definition.
Mini-Mod: Someone who acts like their a moderator of a site, game, etc. . when they really are not. This is usually demonstrated when they point out everyone's mistakes, try to stuff their noses into moderator and administrator business, and act like they are in control, even though they are not.
Goody two-shoes what isn't so good, basicly. These people are not actually considered entirely 'helpful'. However, take note that there is a thick but hard to see line from mini-mods and actually helpful people.