Technically, they did not predict anything at all.
It's just the start of a new b'ak'tun, a new time period if you will.
It will start yet again from 13.0.0.0.0, emerging the 14th b'ak'tun according to the Mayans.
One B'ak'tun is 144,000 days, which equals about 394.5 years.
One B'ak'tun is 20 K'atun, which again is 20 Tun.
Since it's the 14th (since they start from 0), this means that the Mayan would think that the first B'ak'tun started approximately 5523.2 years ago.
I may be wrong in my calculations, but anyhow, that's all there is to it. It's just a change of calendar.
Edit:
Right, did something wrong already. Was a bit to hasty on my calculator, but I have corrected the mistake.