Kneading is a movement in which cats alternate their claws in a rhythmic pattern on a soft material, such as a fluffy blanket or even your lap.
Kneading is a typical behaviour in both juvenile and adult cats, so you've probably seen your cat do it. This is a behaviour that a kitten exhibits from the time it is born. A nursing kitten will instinctively knead to aid the mother's milk flow before they are ready to move about and fend for themselves.
So, you could ask, why does my cat knead me?! In your cat's perspective, you're playing the maternal role, and by inviting him into your lap and snuggling him, you're simulating the security he had with his mother when he was a small suckling kitten. Despite the fact that kneading you does not result in milk, your cat will link the activity with the soothing comfort of nursing. Your cat will continue to knead, purr, and rub affectionately, and most owners will find this to be completely normal behaviour.
Unfortunately, for the human parent, this may be extremely painful, as the happier your cat is, the harder he will dig in with his sharp claws! Try putting a thick, soft barrier between your cat and your lap, such as a fluffy throw, to make things easier for your legs and for both of you. Keeping your cat's claws short by cutting them on a regular basis can ensure long-term comfort for both of you.