What we see in a good game is the seamless blending of theme and mechanics. Not all games do this, (Despite all its goodness, Dominion comes to mind) but once again what we are aiming for is a good game. Having a well executed game can be very good, having a controlling idea coming through will make that game even better.
But first we need to clear up the concept of 'Theme Vs. Mechanics.' Like the Yin and Yang symbol one is inexorably tied to the other. One should think about it as 'Theme and Mechanics.'
Theme is what you are doing in a game.
Mechanics is what you do in the game.*
What makes this formula difficult is that people have a tendency to approach it from one side or the other. They come up with a good mechanic or a twist on a current mechanic, but then are left scrambling to find an original theme. Or, like in my case many, (many, many, many) years ago, I came up with a very detailed world for a game, but could never place a mechanic with it (currently on the 5th attempt).
The way out of this trap is having the controlling idea bind the two elements together. The controlling idea is the nub that the designer will keep returning to see if the game they are building matches what they are attempting to create.
The controlling idea still needs to be translated into theme and mechanics. Put another way, the experience of the Controlling idea needs to carry over, but everything else can change.
For example, the controlling idea for Post Position is for players to have the experience as a day trader on wall street. But look back at my description of the game. Players are members of the mob betting on a horse race. That's a long way away from trading stocks on wall street. But at it's core players are buying and selling (all with a lot of insider information) on items that have an un-programed fluctuating value in a trading floor environment. As long as the game contains those elements (and they still do) then I consider the resulting design to be true to the controlling idea and a success.
At any point during the design process as the theme and mechanics are developing side by side, the easiest way to keep those elements in line and working together is by referring back to the Controlling Idea. Next time we'll look at the translation process of the Controlling Idea into theme and mechanics.
*I am not discounting Abstract games. In an abstract game the theme and mechanics are exactly the same, what I am doing is what I do. I do not have the mindset to pull that off, but I applaud those who do.