Did you ever try to have a staring contest with your cat only to have them blink slowly at you and then avert their eye? It is a very curious sort of behavior with a definite meaning.
Directly staring at your cat can be interpreted as an aggressive behavior. This is because cats use this stare in the wild to threaten or challenge. Cats that have a friendly relationship will rarely look each other in the eyes. If they do, then they typically blink and then look away. This is their way of saying there is no threat and the relationship is one of friendship and peace.
When a cat does the same to their owner it is their way of saying I do not perceive you as a threat but am comfortable with our relationship. It can also be a means of asking for further interaction. When your cat does the slow blink see if they are asking for more. Extend your finger toward your cat and let him decide if he wants to play or cuddle. Cats who wish further interaction will typically rub their face on your finger. If your cat backs away then no further interaction is desired The slow blink is simply your cat’s way of saying she is happy where she is and comfortable with your relationship.