The rule of thirds is the way that someone lines up a shot with tha camera. Its like puting an elongated tic-tac-toe board over the frame and using the lines to posistion the image or video and angle of the subject.

 

 

as seen in the picture above, one of the two images has a great shot, the other, not so much. The picture of the boy is ok, but it lacks focus, the subject is properly placed however, the eyes are where the top right intersection of the lines would be, but the size isnt right. The picture of the flower on the bottom is the better excample of the rule of thirds, the flower falls under the perfect placement if the grid were to be placed over the picture and the angle is perfect for the shot type.