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You've probably heard of it as the Doppler Effect. Essentially, when something is moving away from you the wavelength of light from that object is "stretched" which has the appearance of being more red than it naturally is.
In reverse, an object moving towards you shortens the wavelength making it look more blue. This is blue shift.
For cosmology, if you have a method for knowing what the natural wavelength of light is (and spectroscopic measurements give us that for stars) you can then determine the relative motion between you and that object. Since, when you look out into space, pretty much everything is red shifted that suggests everything is moving away from everything else. And because the red shift is proportional to the distance away from us (things farther away are moving away faster, aka Hubble's Law) that is strong support for the idea that space itself is expanding and is a key underpinning of the Big Bang.
On a much more local level, redshift/blueshift (oneshift, twoshift), is used for many things. One example would be police radar guns. The gun emits light of a known wavelength which hits the target and reflects back to the gun. If that object is moving relative to the speed gun the wavelength of the light will be subtly changed during the reflection. If it is more "red" then the object is moving away; more "blue" and it is moving closer and the amount of change tells you how fast.
Another local use is in the Doppler Weather Radar all our TV stations brag about having. The key different between previous weather radar and the suddenly hip Doppler radar was that it added the ability to measure phase shift and so could "see" wind rather than having to physically measure it on site. So not only could the weather station say "it is raining over there" but also "it is raining over there and moving towards over here at some miles per hour." Even more valuable is that it has allowed for much improved tornado prediction.
Thus ends today science lecture. Please fill out the comment cards before leaving as that is how they decide if I get tenure. I'm sure someone will be along to correct my mistakes if I made any.
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