The Doppler Shift describes a change in frequency of a wave that an observer sees when moving relative to the source of the waves.
A good example of the Doppler Shift is the change in pitch (how high/low a note sounds) we can hear from ambulances as they drive past us. When the ambulance is driving towards us, the sound waves produced by the siren are compressed as the ambulance moves closer and closer. This makes the siren sound much higher than it is. As the ambulance passes us and starts driving away from us, the sound waves are emitted further apart from each other, and so the siren appears to have a lower pitch than it actually has.
This effect can be used to measure blood flow in the body. The device used has a transmitter and a receiver. The transmitter emits ultrasonic waves of an original frequency (f0) which are then directed at a blood vessel. The waves are scattered by the moving red blood cells, and so the returned waves have a different frequency (f') to the original waves, due to the Doppler Shift. This difference in frequency allows doctors to learn about the speed and type of flow in the blood vessel, which is useful for many different areas of medicine.