This three-club rebid distinguishes a really bad hand from one with a little something. The double-negative rebid allows the bidding to stop at three of opener's original major suit.
Responder shows values by bidding anything else.
With a natural club bid, the best he can do is stall with two notrump. Even though you have decent support for opener's suit, your first obligation is to show that you have a terrible hand. Any heart raise would show more overall strength. Here your scattered strength makes you too strong for a double negative. Your natural move is to raise hearts.