The Doppler effect occurs whenever a source of light or sound waves moves with respect to the observer, and results in a change in the wavelength and frequency of the waves. The effect is familiar, for example from the sound of an ambulance that rushes by with its alarm on : the tone of the alarm sounds higher while the ambulance approaches us, and lower when it moves away from us. A bit simplified it appears that the sound waves are "pressed together" when the source of the sound approaches us, and "stretched out" when the source of the sound moves away.
The same happens to light. Here the wavelength of the light becomes smaller, and the light therefore becomes more blue, when the light source approaches us and the wavelength becomes larger, and the light redder, when the light source moves away. This is also the effect which has shown that the Universe expands, from measurements of the redshift of the light from distant galaxies.
The velocity of the oscillations in stars is much smaller than that, but with extremely sensitive measuring techniques it has become possible to measure oscillation velocities on the solar surface as small as a few millimeters per second.