A roleplaying game has the open narrative structure of improv, but is constrained by rules and to make it fair, concise, and to allow for the story to progress. Those contraints are what I call mechanics, and they are how actions or conflicts are resolved within game. Simply, mechanics is the stuff you do (dice, cards, elaborate descriptions, etc) that determines what your characters do, whether the succeed or fail, and by how much.
A good game will have just one core mechanic to deal with all of this stuff. One of the great sins of several (though by no means all) older games was to have multiple mechanics in the game. For example, a game, that shall remain nameless, dealt with combat using D20's, skills using a percentage system, and combat damage using this multi-layered thing with all sorts of multipliers and hit locations. In short the game was, and still is, a mess. In comparison, later games have much tighter rules mechanics that hew closer to my single mechanic rule. Two examples: First, CCP Whitewolf's Storyteller system. Now I have some personal issues with the World of Darkness, but they worked hard to design a single, cohesive dice pool mechanic that works the same for almost everything done in the game, and for the most part, they succeeded. Most rolls to do anything in Whitewolf games are roll a number of D10's equal to Stat + Skill + Other Modifiers, compare to difficulty, determine success or failure. If I can explain it in 1 sentence, then it is probably pretty good, if not great. The second example is the D20 system. Now, I get A LOT of complaints about various aspects of D20, but the single core mechanic of roll 1d20+Stat modifier+Skill/BAB+Other Modifiers versus difficulty is a simple, elegant mechanic that holds up well, even if other parts of the game fall flat.
So now you know what I mean, so why is it important. I will give a 3 reasons: Barrier to Entry, Speed of Play, Clarity of Results.
Barrier to Entry
I think this is the most important of the 3. Whenever some one is learning to play a new game, there is a chunk of time where they have no clue what is going on. Now for savvy, experienced players this time span might be mere minutes, but for young and/or inexperienced players, this can last several sessions or longer. If it lasts too long they will lose interest, and stop playing. Having a single mechanic they need to lear means players spend less time learning the game and more time playing it. Lowering the barrier to entry means more people play games, and I get to keep making them.
Speed of Play
There are those who love the minute details of combat and are glad to spend hours exploring a single combat encounter. And to them I say, "Go and play a strategy game. There are some really fantastic ones on the market." Role playing games should move fast. They are not truly about strategy (though there is some), but are about character, story, narrative, success, failure, and a good time all around the table. Actions and conflicts should be resolved quickly so as not to get in the way of what's going on. Singular mechanics are simple and thus fast. And less time a game spends bogged down with complex rules, the better.
Clarity of Results
There is a certain beauty to a Natural 20. Every gamer knows what it means and what it signifies. In the rules of D&D it is a perfect, unmitigated success. That is clarity. When there is only 1 overarching mechanic in a game, then everyone at the table will have a better grasp of success or failure for anyone's roll. You never run into "that guy" that make's use of obscure optional rules that are mysterious to the other player and don't seem to make a lot of sense (I'm looking at you, 2nd Edition Complete Psionic's Handbook!). A single mechanic that everyone understands enhances everyone's understanding of everyone else's actions, and makes the game better for everyone.
So which mechanic should be the one to rule them all? I don't know. As a game designer, I say, "Mine!". It's got a low barrier to entry, it plays very very fast, and the system for measuring success makes for easy to understand results. Unfortunately, I gotta say that my game mechanic is not right for every game. In fact, I modify bits and pieces of it for each new game I design. There are tonnes of other games out there with very nice mechanics that do what they do very well. Find one you enjoy, and make sure everyone else at the table enjoys it as well.
There will be a part 2 to this mechanic discussion where I talk about resolutions and combat and stuff, so stay tuned.