A cat walks up and rubs its cheek against your leg.
Then its side.
Then maybe its tail.
The behavior is social, but scent is a major part of the explanation.
Cats have scent glands around the face
Important scent glands are located around the cheeks, forehead, lips, and chin.
Other glands are found elsewhere on the body.
Rubbing deposits chemical information onto surfaces and people.
The behavior is often called bunting
When a cat presses or rubs its head against you, people often call it bunting.
The cat is transferring some of its scent while also making physical contact.
That combination can be part of a friendly greeting.
Why mark a person?
Cats build a familiar scent environment.
Objects, furniture, other animals, and people can all become part of that chemical map.
Adding scent to you may help place you inside the cat’s familiar social world.
Is the cat claiming ownership?
“Ownership” is probably too human a translation.
The behavior is better understood as scent exchange and social marking.
The cat is making you smell more familiar.
Why do cats rub when they want food?
Because rubbing also gets attention.
A cat that rubs against your legs before dinner may be greeting you, marking you, and reminding you that the kitchen has responsibilities.
Several motives can operate at once.
Is this related to slow blinking?
Yes, broadly.
Slow blinking is another relaxed social signal cats can use with humans.
Rubbing adds touch and scent to the conversation.
The cat may be saying hello, marking familiar territory, and collecting your scent all at once.
And that’s the short explanation.
Related explanations: Why do cats slow blink at people?, Why do cats purr?, and Why do cats have whiskers?