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.