This rule states that groups of odd numbered subjects/objects are more pleasing to the eye. This is due mostly to the way that our brains process information. When looking at a photograph your brain will organize and process odd numbered groups easier and thus creating the sensation of pleasure. So next time you have 4 apples in your photo just eat one!
Another reason to apply the rule of odds is because often times two of the objects will create a frame and cause the viewers focus to be directed towards the main subject.
For example, take this image which i have also posted in the image gallery on the main page:
As you can see, the two lamps create a type of frame for the photo which ultimately lead your gaze on the woman holding the gun (her extended arms are also on the upper horizontal line of the rule of thirds grid).
One thing to keep in mind is that this rule doesn’t really apply to excessive numbers of subjects. If you have 101 vs 100 people in the photo your brain isn’t really going to care.
TIP: Remember what I said in the post about the rule of thirds? Rules are meant to be broken right? Well if 3 objects make your brain feel a sense of interest why would you ever want to have a photo with 2, 4 or 6 objects? Of course the reason is because you want to purposely create a sense of tension and discomfort. Lets say you are photographing a group of soldiers forming a line who are about to get ripped a new one by their commanding officer. Taking a photo of 4 of them instead of 3 will display that sense of rigidness and discomfort that is more appropriate for that scene. Another example would have you photographing a group of students just before they are about to write a difficult exam. Why would you do this? Maybe to laugh at them later I don’t know. Again, you would get a better sense of the atmosphere in that dreaded classroom by photographing 4 or 6 of them in their perfectly aligned desks while they are chewing those innocent pencils.
Hope that explains it :).
Thank you for reading!