It's perfectly obvious that time has a direction. All we mean by that is that the past is different from the future in lots of different ways. We were younger in the past, we will be older in the future. We remember the past, we don't remember the future.

The surprise is that the difference between past and future is nowhere to be found in the deep down laws of physics. Time is actually a lot like space. If you were out in a space suit flying around, there would be no difference between up, down, left, right. Likewise, there is no intrinsic difference between the past and the future in the laws of physics.

Now that's not completely a mystery to us. We know that what actually happens in the real world is that you're not just made of one or two particles bumping into each other. You're a very, very complicated collection of many, many particles, and they're becoming more disorderly with time. This is to say that entropy [disorder] increases.

The interesting thing is that every difference between the past and the future can ultimately be traced to the fact that the entropy was lower in the past and is growing. That's the Second Law of Thermodynamics. The universe was orderly, it's becoming more disorderly.

And that's not a surprise. There are more ways to be disorderly than to be orderly. The surprise is that the universe was ever low entropy to begin with. If we go all the way back to the Big Bang, 13.7 billion years ago, the universe began in a highly-ordered state. So, modern cosmologists are trying to understand right now why the early universe was in such a precise state, why it was so low entropy.

Once we undertand that, it will make perfect sense to us why the arrow of time stretches as it does from the past, to today, all the way toward the future.