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.

fwiw the rule of thirds was the best setup for my Maggie 1.6s

The 'Golden Ratio" rule is just as important along these lines of thought. The ratio is 1.6 : 1 which was discovered during the Greek times thousands of years ago.

It can be used for room size propotions. For example if the room height is 8 feet, then the room width should be
1.6 times that or 13 feet. If the room width is 13 feet then the room length should be 1.6 times that or 21 feet. This will eliminate certain frequencies from being accentuated in the room.

If the distance from the front of the room to the speakers is 1 then the distance from the left side of the room to the right speaker is 1.6 times that. Same goes for the the other speaker. That will leave a relative distance of .6 between the side of each wall and the closest speaker.

Under these conditions, the distance between the two speakers is 1 as well as the distance from each speaker to the sweet spot is 1, thus forming an equilateral triangle.

This will tell you not only the relative room proportions, but where everything is positioned in the room.

This application of the golden ratio to audio rooms was first developed by George Cardas. You can check out more on this on the internet. Do a search for the golden ratio for audio uses

Enter 'room mode calculator' in google and enter golden ratio numbers and see that there are few bass nodes of note.

As a starting point for an all-new room, this is a very good way to go. Or, even to produce a low-resonance speaker enclosure.

Phi is one of the 'magic' numbers and has been known for centuries. Artists, architects, audio designers, and most importantly Nature herself have all made good use of this number.