Seats around a meeting room table are not all of equal influence.
The smooth transfer of the conversation from one speaker to the next is as much about visual cues as it is about verbal ones. Body language gives us a sub-conscious indicator of where the next input is most likely to arise, and as a result, people's attention will, in many cases, naturally shift to that person.
Of course someone else may 'chip in' or interrupt the flow with an immediately verbal input (as is often the case) but this can appear a little disruptive by comparison, and the need to do so can feel difficult or awkward to people who may be of a quieter disposition. Conversely, engaging people through body language can create a more intuitive flow which confers a natural sense of deference to certain people and positions.
Not every seat around a table has the same visibility. It is generally easier to engage the current speaker's eye (even subconsciously) if you are sat in the red seats in the illustration, than if you are sat in the grey seats. As a result, these seats tend to have more inherent influence about them.
This is often recognised subconsciously also, and so it is not unusual for these more prominent locations to attract the more vocal participants, and for the quieter participants to gravitate toward the corners. This can compound the dynamic since the main protagonists them have a clearer view of each other than they do of the rest of their colleagues, with the main traffic and focus of conversation (the dotted lines) tending to 'cut-off' the corners.
The green seats in the illustration have different levels of influence depending whether the main 'authority' within the room is around the table (and probably in one of the red positions) or whether it is facilitating (or presenting to) the meeting from the open end of the 'U'. In the case of the former, these are quite weak positions, but in the case of the latter they have a better chance of catching the facilitator or presenter's eye, although still not as easily as the red positions.
How might this information be useful to you?
In the first case, simply being aware of it can provide insight into the dynamics of your meeting, and the impact that where people choose to sit may have on the outcomes, and the ownership of those outcomes.
Beyond that, you can use this insight to decide whether intervening in the seating arrangements could have any bearing on the outcomes, and whether there may be more productive configurations of who sits where. This may involve using name-cards to move people about from meeting to meeting, and pulling those who have the most valuable insight for the topic at hand more toward the centre of of each side (particularly if they are quieter people by nature).
The illustration in this article is for a U-shape table arrangement, because that arrangement is the most useful for productive meetings of a larger group. However, the same principles can also be applied to board-room table layouts and other arrangements. See meeting room setups.