Knowing why your cat behaves in certain ways, helps you form a closer bond with your pet.

Rubbing

Cats love to rub their faces against corners, cabinet doors, and your legs. They rub against things because they are leaving their scent on their surroundings. Cats recognize each other through their scent. Rubbing is also a special greeting from your cat.

Purring

Purring is the soothing way mother cats talk to their kittens. Cats continue purring as they grow into adulthood as a sign of contentment. When your cat purrs, it means he's happy.

Kneading

Sometimes your cat will begin kneading your lap when she is sitting on you. The cat spreads her paws which pushes out the claws and digs them into your lap, one paw after the other. Your cat is not trying to hurt you; rather it is a behavior from when she was a kitten. Kittens knead their paws when they are nursing. When the cat is an adult, kneading means she feels safe and warm in your lap just like when she was nursing from her mother.

Spitting up Hairballs

As your cat washes himself, his rough tongue pulls dead fur out of his coat and he swallows some. Most of the hair passes through the stomach as the cat digests but some of it forms a ball in the cat's stomach. When your cat throws up the hairball, it is a good thing but when the hairball passes into the cat's intestines it causes problems. Cats sometimes eat grass which helps them digest the hairball. Often, a hairball blocking the cat's intestine has to be removed with surgery. Brushing your cat every day helps stop hairballs from forming.

Flattened Ears

When your cat holds her ears flattened to her head and her eye pupils are opened wide, it means she is afraid. Crouching down and fast breathing are also signs of fear. When your cat is afraid, she will try to reach high ground, like the top of a refrigerator on top of a closet shelf.

Source:
University of Illinois, College of Veterinary Medicine: "Why Does My Cat Do That?"
Cornell University, College of Veterinary Medicine: "A Hairy Dilemma"