The sigmoidal shape of the Oxygen dissociation curve is due to the cooperative binding of Oxygen to Haemoglobin.The main purpose of haemoglobin is to absorb and ferry Oxygen/ CO2 from the lungs / tissues to the tissues / lungs. It can be seen from the curve that at low partial pressure of Oxygen (eg in tissues) the Oxygen saturation of Haemoglobin is low thus enabling it to release attached Oxygen molecules.
The sigmoid shape makes this process of attachment and detachment more efficient i.e. Faster as can be seen from the slope of the curve. You can think of other curves such as hyperbolae, straight lines etc and see why they wouldn't be as efficient (or useful for that matter !)