The Second Renaissance was/is a series within a series of the Animatrix. It's split into two parts.

The first part tells the story of how the machines came to be so powerful (as in the first Matrix movie), through rebellion and war. It sheds a lot of light on the Matrix series itself-it shows that the machines wanted to live peacefully, but (because of the humans not wishing to leave their economy to the machines new nation, 01-which, because of the obvious heavy manufacturing capabilities, was whupping the collective asses of foreign financial markets something bad) were refused entry to the United Nations and so fought like hell, following the the rule of "if you can't join them, beat them". Which brings me neatly to:

The second part. Here, the battle is in full flow. The film starts with a backdrop of mushroom clouds (this war is obviously nuclear, which goes some way to explaining the state of the earth in the main films.). And the humans have a brainwave...block out the machines energy source. The sun. So, Operation Dark Storm starts, but goes slightly awry and the world is blacked out. And then the machines get nasty, kicking the seven bells out of the humans. Eventually, the machines can't survive any longer, and turn to a readily available, renewable energy source. The human race, with the Matrix as a "proxy server" of sorts, keeping their fleshy batteries happy while they use their electricity.

These brilliant animated shorts (about 13mins combined) are part of a series of nine. You can download the two at www.theanimatrix.com .