Of course, as a modern, sophisticated society (certain recent events notwithstanding) we understand that the eclipse is just a matter of interplanetary physics and the odd coincidence that our unusually large moon is at precisely the right distance that it appears to us to be almost exactly the same size as our sun. But imagine what our distant forefathers must have thought about the sun disappearing; I’m guessing complete and utter terror followed by, if all those warnings about not looking at it are correct, blindness. Little wonder that ancient civilizations put so much time and effort into tracking celestial bodies and trying to predict things like eclipses.
Although someone really paying attention would begin to notice the sun slowly disappearing, the easily noticeable effects start about 15 minutes before totality, when the quality of light on earth starts to change. Everything gets darker and darker minute-by-minute. There will be a sudden drop in temperature and wildlife, especially birds, will start to go quiet as they notice the odd change of light.
Just before totality, things start to get surreal. It doesn't feel like day, but it's not like night either. Nor is it like dawn or dusk. It's an eclipse. Depending on the atmospheric conditions the sky can start to display some unique colors. And if you’re up high on a mountain or have a good view of mountains to the west, you might be able to see the edge of the moon’s shadow moving across the land.
Perhaps the most unique phenomenon that can happen just before and after totality are shadow bands. These are faint and mostly noticeable on smooth, flat and light colored surfaces. They dance around and are best compared to the shadows seen on the bottom of a swimming pool.