The guys who found this in ~1965, Arno Penzias and Robert Wilson, hated it- they were trying to use a large antenna owned by Bell Laboratories in Holmdel, NJ when they were pestered by this annoying background noise. Oddly enough, about 30 miles away at Princeton University, Robert Dicke and his team were doing everything they could to identify this mysterious CBM...they eventually met up and published two papers on the subject. To give credit, the idea was originally postulated by George Gamow in the 1940s. Penzias and Wilson received the Nobel Prize in 1978 for their work.
But back to the why- or perhaps the how, rather. A quick refresh on radiation. The electromagnetic spectrum measures radiation based on its' wavelength (which determines its' frequency). I've posted a quick link to a video that explains this much more elegantly, but it's basically this: radio waves have a long wavelength and x-rays/gamma rays have short wavelength and the light that we see- virtually everything we see- is in the middle (energy increases with decreasing wavelength- this is why some rays are more powerful- and harmful- than others).
Next topic- the Doppler effect. This is when waves can become longer or shorter based on the distance that they are projected from, more or less. Think of a fire truck moving towards you with its' sirens on - at first you hear a very long siren, but as it approaches the sounds begin to increase in frequency, and thus become higher in pitch (called blueshift). If the fire truck were to be moving away from you, it would decrease in pitch (called redshift). Blue and red just refer to the direction of the shift on the electromagnetic spectrum. Wikipedia has an awesome video on the main page describing this.
Finally, here we go. This is a simple version of how CBM came to be. When the universe began, it was much smaller, denser and hotter- not to mention there was a lot of very bright light. The theory has it that Earth is always moving away from the big bang (please don't ask me to explain this- maybe I'll post another entry on this soon). As the universe expanded, it began to cool and the same photons of light had to occupy a larger space. So, if the Earth is moving away from all of this hot, bright light and cooling, we will perceive this light as being redshifted as we move away. In fact, if we move away for billions of years (how old do they figure now, 13.7 billion years or something?), the redshift can be enormous! We may actually perceive this bright light as radio waves. Low and behold, the vast 'emptiness' of space that surrounds the Earth is filled with radio waves in the form of cosmic radiation from the big bang.
The next time you turn on the television, try tuning to a station that you don't recieve a signal for. About 1% of the static that you will see is cosmic background radiation. In the words of Bill Bryson, the next time you complain about there being nothing on TV, just sit back and enjoy watching the birth of the universe.
Finally, a favorite quote of mine about the development of the universe by Edward P Tyron.