The title comes from a quote in the first film, when Morpheus is telling Neo the truth about the nature of the Matrix he says:
"We have only bits and pieces of information but what we know for certain is that at some point in the early twenty-first century all of mankind was united in celebration. We marveled at our own magnificence as we gave birth to AI."
It was planned to be retold in The Animatrix as the first of four parts, but the other three were never made. Instead the story became "The Second Renaissance", which retells the story of Bits and Pieces of Information and continues where it leaves off.