Many people think cats are asocial, but in fact they are very social animals. They bond with other cats in their house or neighborhood, their owners, even other pets like dogs and birds. They communicate to each other and us a variety of ways.
A keen sense of smell is important in cat communication. When her human returns home, a cat carefully sniffs then proceeds to rub her face against owner's legs. She is placing her scent on you, marking you as her territory. As you have gone through your day, scent molecules have attached to your clothing. Your cat must mark you again to cover up those other smells.
Cats also communicate through body language. Your cat's posture, gestures, facial expressions, tail, ear and whisker position can all be aan indication of how your cat is feeling.
A bristling tail held straight up, or one that thrashes back and forth are warnings. If a cat is feeling defensive, tail is usually arched. Hissing and backing away with ears flat against head are other defensive poses. You can tell a lot about a cat's state of being from its eyes. Wide, dilated eyes communicate anger or fear. A contented cat slowly blinks its eyes, or keeps them half-closed.
There are probably many more movements that send signals, but they are so subtle, only another cat can notice and interpret them. This explains why cats seem to "read one another's minds." Two cats might gaze at each other without moving for a very long time, then suddenly erupt into action. What was signal? A twitch of lip, lift of a lip, tilt of head? Only cats know.