In this photo the left top intersection aligns with her eye which pulls the focus to her eyes and face, and her ear is on the right third which pulls attention to her ears and earrings.
For this one the subject is Ryan and his head is on the top right intersection of the photo, the left intersection lines up with the left vertical line, which adds to the feeling of isolation.
In this one the mini library and the car line up with the two bottom intersections which draws attention to them Also the roof of the porch lines up with the top third which draws attention to the house.
The rule of thirds is a way to draw attention and utilize design. Humans are hardwired to find thirds pleasing so photos with subjects aligned with thirds look more artistic and pleasing to look at. An image that uses the rule of thirds will look much more natural and comfortable to the viewer.