The flow of time is both mysterious and not very mysterious.
The not-very-mysterious explanation. Let's take a situation in which you have an ice cube sitting in a puddle of water on a hot slab of concrete. As far as the laws of physics, the following two futures are both possible:
- The ice cube gets smaller and the puddle of water gets larger and the concrete gets cooler.
- The ice cube gets larger and the puddle of water gets smaller and the concrete gets warmer.
So why is it that we only see #1 and not #2? That's actually not mysterious. There are an enormous number of ways you can assign velocities to the water molecules in the ice and puddle. The vast majority of those choices will lead to the ice melting in the future. So it is almost certain that the ice will melt.
So that's not mysterious. But back up a little further, and ask why was there a block of ice sitting on a slab of concrete, in the first place?
THAT seems enormously unlikely, as well.
So that's the mysterious and non-mysterious sides of the question. Given that the universe is the way that it is, with hydrogen to burn in stars, and with plants to absorb light to grow, and with creatures to eat the plants, etc., it's very likely that events will unfold in one direction only: the direction of increasing entropy. So that's not mysterious. But the fact that the universe started out having a very low entropy is mysterious. I don't think there is a consensus about why it should be that way, other than: that's just the way it is.