​The audible vibration that we love so much, purring, is a bit of a mystery still, but most research shows that it is a result of the larynx (voice box) and diaphragm (main muscle used for breathing) working together via signals from a cat's brain.  It is thought to originate as a soothing sound from the queen (mother) cat to her kittens.  However, cats will continue to purr in life when they are feeling affectionate or loved.  Some will purr to sooth themselves when asleep, injured, sick, or even nervous.  Just like each cat is an individual, each cat has its own characteristic purr.
 
We do know that purring is an intentional thing which cats, even wild ones, do on purrrrpose.  So when your sweet furry friend rubs against your leg or hand, or jumps in your lap, you should be flattered and charmed--and reciprocate with their favorite forms of affection that you know they love.