Cats, unlike dogs, have a variety of behaviors that we humans just don't understand. They are enigmatic creatures with their own set of instincts, feelings, and reactions, and so it can be tough for the cat owner to understand why the cat does what it does. So here's a little breakdown of common cat behaviors.
The ready to pounce quivering butt: Cats wiggle back and forth to position themselves for the perfect attack.
Rolling back and forth: Your cat is showing submission or inviting you to play.
Sticking a raised butt in your face: Tail sniffing is normal in the cat world, so this is your cat's way of saying hello.
Making squinty eyes: Cats squint when they're content. Closing their eyes slowly is a sign of trust. Try to slowly blink at your cat, it's a friendly gesture of trust.
Cats sleep in a circle to conserve body heat.
Sitting like a cat loaf: Cats tuck their paws under them when they feel safe, and it also conserves body heat.
One leg extended: This just makes it easier for your cat to clean. And of course to show off how flexible it is!
Staring into space: Cats have keen senses, so they probably saw a fly or a speck of dust. 
Exposing its belly: Since the belly is the most exposed area for a cat, this is an enormous show of trust. Don't confuse this with a cat on its back defending itself. The show of trust is letting you touch the belly.
Sleeping in boxes: Cats are always mindful of protecting themselves, and so they find security in confined spaces. A box is exactly that. 
The “hug ‘n’ bite”: Biting and wrestling with you is actually not a sign of aggression but of playfulness. Cats forget we don't have fur to protect us from their teeth and claws.
Chirping or clacking at birds outside: The clicking and chattering is a sound a cat makes when it's concentrating on a target for the hunt, they often make it out of frustration that they cannot reach it.
Sitting on your computer: Cats like warm places. Also, they want to annoy you. 
Nowhere to be found: Cats are good at hiding, and they're sometimes tired of humans and their weird ways, so they find a great hiding place and stay there for a while. Be patient, they'll come out eventually.
