Cats send all sorts of nonverbal signals, both to each other and to us humans. One of those signals is a blink.
If you own a cat and haven't ever noticed it blinking at you, keep an eye out. It usually happens just as the cat enters a room where you are sitting. It will notice you from a small distance, stop, blink both eyes once or several times, and then approach. Once you are on the lookout for it, the blink is quite noticeable. It's slower than a human blink and looks, well, intentional.
What is your cat trying to tell you? A blinking cat is a happy cat. Blinking in cats is a signal that they recognize the presence of another cat in their vicinity, but they are not going to fight it. A blink sends the message: "You are my friend. I am not angry. I am not threatened, or threatening."
This kind of message is very important in the wild, where cats battle for territory. Run across a neighboring cat and you'd better make your intentions clear, or you may find yourself in a fight. The blink serves to say: all's well here.
If you don't feel silly doing it, try blinking at your cat, perhaps while stroking it. Sometimes our facial gestures can trigger a response in them. The two of you can have a mutual friendship moment, sending "I'm okay, you're okay" messages back and forth.