Cats often stare as a way of communicating with us. They may be trying to tell us that they're hungry, thirsty, or need to go to the bathroom.
Cats are also naturally curious creatures, and they may stare at us simply because they're trying to figure out what we're doing.
Sometimes, cats stare as a way of asserting dominance. This is especially common in multi-cat households.
In some cases, cats may stare if they're feeling stressed or anxious. This is especially common if the cat is new to their surroundings or if they're feeling threatened.
In rare cases, cats may stare if they have a medical condition, such as hyperthyroidism or a brain tumor.
Sometimes, cats stare for no reason at all. They may just be daydreaming or enjoying the view.
If you're ever unsure why your cat is staring at you, the best thing to do is to simply ignore them.