The apparant frequency of radiation is affected by relative motion between the source of the radiation and the observer of the radiation. If the source and the observer are moving towards each other, the observer measures a frequency higher than if there were no motion; if they are moving apart, the measured frequency is lower. This phenomenon is called the Doppler effect. The change in frequency is called the Doppler shift. The size of the shift tells the speed. The Doppler effect is common to all wave phenomena. You may have noticed it with sound; if you ride a motorboat towards the waves you hit a lot more of them in a second than if you travel with the waves; it's the basis of radar measurement of automobile and baseball and tennis ball speed.
In astronomy the effect is usually made apparant through the use of a 'comparison spectrum.' That is the spectrum produced by a light source in the observatory-that is one not moving relative to the observer. The spectrum of the star is compared to this spectrum, and the Doppler shift shows up as a very small separation between the lines in one spectrum and those in the other. If the star's lines are on the low frequency side of the comparison lines (that's toward the the red) the shift is called a 'red shift.' If the other way, it's a 'blue shift'. The red and blue refer to direction, not color. A star whose light is red-shifted is not (necessarily) a star that looks red.