3dB is the smallest perceivable difference to the human ear.
I was not able to find any reference that says that, or in fact that links any dB number to that description. I was able to find this (http://en.wikipedia.org/wiki/Decibel):
"A change in power by a factor of two is approximately a 3 dB change."
The dB is a mathematical construct, not a measure of what is audible or discernible by human hearing. I have always heard that an increase of 6dB is roughly equivalent to a doubling of apparent volume, but I didn't see that, either.