Minmaxing is the art of minimizing your disadvantages and maximizing your advantages in a game. Mostly done in roleplaying games, where it's used with a bit of a derogative term. In fact, terms I've heard which are supposedly synonymous are munchkin, powergamer, points whores (for systems which use a point based construction), rules rapists, and some which are probably not fit to see print. (It is an art best practiced by a good rules lawyer.)
There is a talent to good minmaxing, which separates good powergamers from mere munchkins. There's a line you have to walk, which allows you to have a harmlessly powerful, yet still fun and interesting character, as opposed to simply a set of good numbers written on a sheet of paper.
An example, that's on the other side of that line than I like to walk, is from a character from one of my players in my old Shadowrun game: A night-one (sensitive to light, bonus to charisma and willpower), albino (sensitive to light, bonus to willpower), with an allergy to sunlight (sensitive to light, bonus to willpower), owl shaman (can only cast spells at night, penalty for casting spells at daytime). Since most of the game of Shadowrun happens at night, this character rarely has a problem. But, the character avoid contact with people during the day, and pretty much all the time, in fact. There doesn't seem to be any personality other than, "I can summon really big spirits and cast really impressive spells at night time."
Another example can be found in the writeup for keen vorpal scimitar +4, but this example is still within the limits of "benign minmax." The new edition of Dungeons and Dragons has a very pro-minmax attitude, while still maintaining a semblence of a game. At the GenCon where they introduced the game, they also gave a few seminars on how to minmax. The benefit of this is that it allowed the dungeon masters who are going to have to deal with the minmaxers the same information, so that everyone knows what to expect.
Minmaxing only has a derogative reputation because it introduces inequality inside the party. Characters who were created for roleplaying value are nowhere near as powerful as characters created merely for points, but you can strike a comfortable balance between the two.
One of the players in my D&D game is a benign minmaxer. I know that I can expect an interesting character from him, a good story, and effective use of powers. Since he does know the rules enough to make effective characters, he can also provide me with help in rules questions. And when a new player is introduced to the game, I can have him aid the new player in how to effectively spend their points. (Interesting note, one day, one new player noticed he was wearing an "IMAX" theatre shirt. We laughed at the appropriateness of the shirt: I MAX.)