The Earth rotates in an eastward direction, known as prograde rotation. If you were looking down on the Earth from above the North Pole, it would appear to be spinning counterclockwise. Therefore, if an airplane travels from Singapore to New York in a clockwise direction, it would reach its destination faster compared to a counterclockwise route.
Does flying an airplane opposite to the Earth's rotation direction save fuel & time?
It is actually the opposite way around. Note that the velocity relevant for fuel consumption is not the absolute velocity of the plane, but the velocity relative to the air it is travelling through.
Assuming that the earths' atmosphere rotates with the same speed as the earth's surface, it does not make any difference whether you fly east or west.
However, due to the coriolis effect there are wind tubes called jet streams that point eastwards. Airplanes can take advantage of this and save fuel by flying within the jet stream, e.g., when travelling from NYC to Paris.
