The new year begins after midnight. Midnight being 12:00 AM or 2400 hours, and nothing happens after 2400 hours because that's all there is. Just 24 hours.

A simple analogy would be...
if you have a piece of pie, that's today. You eat the pie, and when it's all gone, your day is done. But hey! There's another piece of pie which you can start to eat. Maybe that's not the best analogy in the world.

Time is a bizarre concept. We can all pretty much agree that time, it is a precious thing, along with all its splendors, along with all its joys.