I keep reading that a smooth curve, say r(t) = (x(t),y(t)), is a curve such that r'(t) is continuous and r'(t) \neq 0.

I understand the "r'(t) is continuous" bit - so there are no "kinks" or anything in the curve (hence, smooth), but I don't understand why we require r'(t) \neq 0. Would anyone be able to explain this part to me please?