Why do cats stare at us?

In fact, a cat stare is friendly. It means that you are the center of their universe. It means that you are the most interesting being in their life. It is a symbol of love. It could also mean that their food dish is empty, but it is mainly a love stare.
When you find your cat staring at you, give them a 'slow blink.' A slow blink is the equivalent of a cat kiss. Cats are very big on body language. Show your cat that you find them interesting as well. Smile at them, pet them, and talk to them. It will make their day, along with some quality playtime.