The riddle
What Has 13 Hearts but No Other Organs?
Counting the suit
Fifty-two cards make up a standard deck, split into four suits: hearts, diamonds, clubs and spades. Each suit has 13 cards, the ace, the numbers 2 through 10, and the jack, queen and king. That makes 13 hearts: ace through 10 is ten cards, and three face cards bring the suit to 13. Four suits of 13 give 52. Britannica describes the most widely used deck in just those terms.
Why the organ joke works
A heart on a card is only a shape. A real heart is an organ that pumps blood. The riddle treats the red symbol as if it were the real thing and then adds "no other organs", which makes the listener hunt for a creature with 13 hearts and nothing else. The number 13 is the genuine clue, because it is the size of one suit.
More counts in the same deck
Hearts and diamonds are red and clubs and spades are black, so the deck splits evenly into 26 red cards and 26 black ones. Many packs also carry two extra cards called jokers, which brings the total to 54, though a joker belongs to no suit.
Showing it off
This is a riddle to ask with a deck in hand. Sort the cards by suit into four piles, count one pile and the answer is lying on the table. Turning that pile over one card at a time shows every rank from ace to king.