what is the rule of thirds?

Divide your room into thirds creating a grid. Then place you speakers on the 1/3d line (from the wall behind it). Bring your listening spot (your ears) out to the 1/3d line from the rear wall and equal distance from each speaker, thus creating a triangle.

That would ONLY be a starting point and would unlikely ever to be the best place except in a 'perfectly' designed room. For example, in my room which has a length of 19.5 ft my speakers are 66 inches from the wall behind them and my listening position is about 60 inches from the wall benind my chair.

FWIW.

I believe the former editor of TAS likes to take credit for identifying this concept but I think it has been known for some time, he was just the first one to publicize it. Other odd dimension fractions have been recommended as well - 1/5, 1/7, etc. Since another basic rule of acoustics is to avoid square rooms (equal dimensions maximize room nodes), assuming the room length and width are different, applying a fractional multiplier like 1/3 will result in different distances from the front and side walls which should also provide a benefit.

As Newbee points out, you should be just as concerned with your listening seat placement as with your speaker placement.

While the rule of thirds is a good starting point for most, that's all it is; a starting point. It assumes that one is using a desirable room w/o even multiple dimensions. And that might be the best premise of this guide, using uneven dimensions that don't have even multiples of any dimension. For example a rule of fifths might work in a desirable room or a combination of odd multiples might work better in a less than desirable room.

Pryso, you beat me to it.
I'm not sure, but I believe that Peter Walker of Quad fame might have been one of,if not the first to promote the "rule of thirds".
If at all possible, if one can avoid even multiples from ceiling, floor as well as length and width it might be beneficial.