Why Do Cats Knead?
Kittens push rhythmically with their front paws against the mother cat's breasts. This stimulates the release of milk. Called kneading because it resembles the way bread dough is made, the behavior carries over into adulthood.
Many felines knead against soft objects when they seem to feel particularly happy and satisfied.
Although we can't know for sure, we suspect the emotions hearken back to feel-good moments of nursing during kittenhood. So adult cats who knead an owner's lap may actually be declaring their love for a surrogate human "mom."
Kitty uses paw-pats to test objects for safety. Soft tentative taps measure temperature, texture and more and also can be used for head-bop discipline, or invitation to play when aimed at other cats. Cats also gently paw human cheeks or mouths during interaction.
Rear Foot Treading
Cats rear-paw tread rhythmically from foot-to-foot for a couple of different reasons. Whole kitties do this after they've mounted the female during breeding, for example.
But both boy and girl cats demonstrate rear foot treading during play. It looks sort of like a "rev your engines" preparation for a chase-and-pounce game, and is also used during hunting when preparing to launch an attack after prey.
Some cats also use rear paw scraping after urine spraying. Kicking up some dirt not only leaves scent marks from paw pads, it may also leave visual cues. These scent and sight cues warn trespassers that the territory is already owned by an alpha cat.