Cats looking out the window is analogous to watching a large screen TV. Birds, squirrels, passing cars, people or even waving branches can enthrall cats by the window for hours. They are fascinated by anything that goes on outside.
If they see something flying swiftly in front of them or a rodent moving quickly across the ground, they will perk their ears and watch attentively.
You can make the "TV" more interesting by adding a bird feeder outside the window. Your cat could sit there and watch for hours.
Why do cats like to sit in the window and watch what goes on outside?
They are natural predators to animals such as birds, rodents and insects. Unlike dogs, cats like to invest time in studying critters before they attack. The reason of this behavior is due to their instinct to prevent themselves from falling into a vulnerable or dangerous position. Also, cats are curious by nature. Even though they may not want to be in contact with a stranger, they are drawn to watch what people do.