It's around because the universe is still around.
Any matter with a non-zero (thats pretty much everything) temperature spontaneously emits e/m radiation(plotons) in a frequency spectrum called a blackbody.
The sun's output peaks in the yellow-green, a human body somewhere in the IR and the visible universe, in the microwave spectrum. Before MAP there was COBE and it fit with high precision and accuracy the measured spectra to a perfect blackbody at 2.73 K.
So mostly it's just the result of the average temperature of the universe, the evolution of which is affected by the expansion.
See here...
http://hyperphysics.phy-astr.gsu.edu/hbase/bkg3k.html#c1