Bigger tires will cause your speedometer to register a speed that is slower than your actual speed. For example, if your speedometer says 35 miles per hour on 20-inch diameter tires, changing to 23-inch diameter tires will make your true speed 40.25 mph, even though your speedometer will still show 35 mph.
The difference in the speed shown by the speedometer and the true speed of the vehicle is due to the change in the distance traveled through each rotation of the tire. A tire with a 20-inch diameter has a circumference of 62.8 inches and will cover 62.8 inches in one rotation. A tire with a 23-inch diameter has a circumference of 72.2 inches and will cover 72.2 inches in one rotation.
Car manufacturers calibrate the speedometer to take into account the specific circumference of the tire on the car when it is originally built. When changing to a bigger tire, the speedometer will still be calibrated for the smaller circumference and will continue to account for the shorter distance covered by each rotation. For this reason, whenever you replace your tires with a size that is different from the original factory installed tires (either bigger or smaller) the speedometer should always be re-calibrated by a qualified mechanic.