Astronomers often use the term redshift when describing how far away a distant object is. To understand what a redshift is, think of how the sound of a siren changes as it moves toward and then away from you. As the sound waves from the siren move toward you, they are compressed into higher frequency sound waves. As the siren moves away from you, its sound waves are stretched into lower frequencies. This shifting of frequencies is called the Doppler effect.
A similar thing happens to light waves. When an object in space moves toward us it light waves are compressed into higher frequencies or shorter wavelengths, and we say that the light is blueshifted. When an object moves away from us, its light waves are stretched into lower frequencies or longer wavelengths, and we say that the light is redshifted.

In the visible portion of the electromagnetic spectrum, blue light has the highest frequency and red light has the lowest. The term blueshift is used when visible light is shifted toward higher frequencies or toward the blue end of the spectrum, and the term redshift is used when light is shifted toward lower frequencies or toward the red end of the spectrum. Today, we can observe light in many other parts of the electromagnetic spectrum such as radio, infrared, ultraviolet, X-rays and gamma rays. However, the terms redshift and blueshift are still used to describe a Doppler shift in any part of the spectrum. For example, if radio waves are shifted into the ultraviolet part of the spectrum, we still say that the light is redshifted - shifted toward lower frequencies.

The light from most objects in the Universe is redshifted as seen from the Earth. Only a few objects, mainly local objects like planets and some nearby stars, are blueshifted. This is because our Universe is expanding. The redshift of an object can be measured by examining the absorption or emission lines in its spectrum. These sets of lines are unique for each atomic element and always have the same spacing. When an object in space moves toward or away from us, the absorption or emission lines will be found at different wavelengths than where they would be if the object was not moving (relative to us).

The change in wavelength of these lines is used to calculate the objects redshift. Redshift is defined as the change in the wavelength of the light divided by the wavelength that the light would have if its source was not moving (called the rest wavelength).

Redshift = (Observed wavelength - Rest wavelength)/(Rest wavelength)

Cosmological Redshift
The cosmological redshift is a redshift caused by the expansion of space. As a result of the Big Bang (the tremendous explosion which marked the beginning of our Universe), the Universe is expanding and most of the galaxies within it are moving away from each other. Astronomers have discovered that all distant galaxies are moving away from us and that the farther away they are, the faster they are moving. This recession of galaxies away from us causes the light from these galaxies to be redshifted. As a result of this, at very large redshifts, much of the ultraviolet and visible light from distant sources is shifted into the infrared part of the spectrum. This means that infrared studies can give us much information about the ultraviolet and visible spectra of very young, distant galaxies.