Morpheus tells Neo:
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 A.I.
Agent Smith says:
The Matrix was redesigned to this, the peak of your civilization. I say your civilization, because as soon as we started thinking for you it really became our civilization, which is of course what this is all about.
So there you have it -- the machines wanted to recreate a time that provided as much technology and "modern life" as possible while still ending prior to the advent of artificial intelligence -- and then restarting at some other (unspecified) point early in the computer age.
(I can only imagine the complications that would arise if a human-created A.I. would be invented within the Matrix simulation -- one possibility is that it would by its nature become aware of the simulation and inform its human creators.)