Why cats purr?

Purr – Wikipedia

Above all, the purr is probably the cat’s way of communicating to others (cats and humans) that it is in the mood to be sociable. The purring sound is frequently made at the same time that other ‘sociable’ signals are made, e.g. erect tail, slightly closed “contented” eyes. Naturally, in most situations, this will also be when the cat is feeling contented, but it need not necessarily be so. Humans usually interpret the purring of a domestic cat as an expression of some type of friendliness or contentment. This assumption is based on the observation that cats often (though not always) purr when being stroked by humans, combined with the experience that human children tend to enjoy stroking by their parents and interpret it as a gesture of affection. Consequently, most humans enjoy listening to or holding a purring cat.