You may be familiar with the Doppler shift already.  When a police car or ambulance goes past you with its siren on, as it passes you the pitch of the siren changes from higher to lower.  For sound waves, the pitch is the frequency of the wave.  But the same effect holds for any wave, including light.

The below animations demonstrate the shift.  The two sources are continuously emitting waves, but the one on the right is moving as it does so.  For an observer that it is moving towards, the waves appear to be bunched together - in other words, the observer measures a shorter wavelength if the wave source is moving towards her.  An observer on the left side of the moving source will measure a longer wavelength because the wave source is moving away from him.

 
 
So if, for example, a star is approaching you, its spectrum is shifted towards higher frequencies or shorter wavelengths.  If the star is receding from you, its spectrum is shifted to lower frequencies or longer wavelengths. 

A star in a binary orbit will be moving away from you for part of its orbit, and moving towards you for the other part, so that the spectrum will shift back and forth in wavelength in a periodic way.

In the Atomic Spectra lab we learned that stellar spectra show the spectral lines of the elements that make up the star.  Below is a spectrum showing where lines of Hydrogen appear.  Remember in that lab we saw these lines as emission lines - Hydrogen has a prominent red line and a blue line.  On the right, the spectrum is shown as a plot of brightness (or intensity) vs. wavelength, with the absorption lines showing as narrow downward spikes.

 
So when a star is not moving towards or away from you, the lines are at their usual wavelengths:

When the star is moving away from you, the spectrum is shifted towards longer wavelengths, that is, in the red direction:

And when the star is moving towards you, the spectrum is shifted towards shorter wavelengths, or the blue end:

We will use this red-shifting and blue-shifting to monitor the motion of binary star orbits.

Remember: The only time we see a Doppler shift is when an object is coming toward us or going away from us! The faster the object moves, the greater the shift.