Cats stare as a way of communicating with their humans. They may be trying to tell you something, such as that they are hungry, bored, or want to play.
Staring can also be a way for cats to bond with their humans. When they stare at you, they are essentially saying, "I'm paying attention to you."
In the wild, cats stare at their prey as a way of sizing them up and preparing to attack.
If a cat is feeling scared or anxious, they may stare at you as a way of trying to figure out what is going on.
If a cat is feeling irritated or annoyed, they may stare at you as a way of showing their displeasure.
In some cases, staring can be a sign of a medical condition, such as hyperthyroidism or cognitive dysfunction syndrome.
Sometimes, cats stare for no reason at all. They may just be curious about what you are doing or thinking.