On Monday evening this week I managed to do a bit of time travelling while driving back home. I was driving back through one of those heavy showers that have been marauding around the place recently, with windscreen wipers full pelt on a rather wet road. However, these showers don't last for very long, and the rain soon began to ease. As it did so, I noticed the road was getting drier. Then the rain stopped all together, and I was left driving on an absolutely dry road.
That's not what usually happens. Usually, the more rain there is, the wetter the road gets. I'm sure you've worked out what was happening. I was heading in the same direction as the shower, but going faster than it. So I had overtaken it, as it were, and emerged from the rain ahead of the shower. There was a dry road, because the shower hadn't got there yet. Sure enough, I got home in the dry but within a few minutes it was raining - the same shower that I'd just driven through.
So I was experiencing the events of the rain shower backwards, because I was travelling faster than it. In one sense it was time travel. I was seeing events happen in a different order from what someone stationary on the ground would have seen.
Of course, it wasn't really time travel. My clock was still going forward, as was everyone else's. Now, if I'd been travelling faster than light, things might have been a little different. Special relativity says that time slows down for an observer travelling quickly (from the point of view of someone who isn't). As this traveller approaches the speed of light, special relativity says that the passing of time for him becomes very slow indeed. In fact, at the speed of light, time wouldn't pass at all for him. That's one of the reasons that photons, light 'particles', behave very oddly.
What about beyond the speed of light? Physics as we know it doesn't let us go there, not even with those neutrinos at Gran Sasso. If that result had been true, our understanding of physics would have been shaken up quite severely. The possibility of really travelling backwards in time might then have become a reality.
[ For those who are more mathematically inclined, the rain shower's also an example of why the partial derivative is not the same as the full derivative. The full derivative for the rate of change of road wetness with respect to time was negative here - the road was getting dryer as I went alogn, but the partial derivative of road wetness with respect to time at constant position was still positive. ]