When the temperature of the primordial plasma was low enough to allow electrons stick to nuclei, the Universe become transparent for light and the radiation decoupled started to wander around the Space. In the adiabatic expansion this radiation cooled down. Now its temperature is 2.73 K, corresponding to microwaves. In 1964, Penzias and Wilson, two engineers of Bell Telephones, working on communication with a satellite, observes a strange noise. They got Nobel prize for it in 1978.
If You observe a picture like this on Your TV, do not
change the channel. This can be a hidden massage from
distant civilizations, and for sure 1/3 of this noise comes
from the Big Bang fossil radiation.
The light that is reaching us has been stretched out as the universe has stretched, so light that was once visible now is reaching us in the form of microwaves.
COBE in 1990 and WMAP in 2003 showed not only that Universe started as a ball of wriggly plasma but also that it is flat to the most remote corner.
A microwave map of the whole sky made the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR).
http://map.gsfc.nasa.gov/m_mm.html