So why do people say it's dangerous to look at a solar eclipse? Well, in general (during non-eclipse times), you've probably been told not to stare at the sun. This is because the sun simply outputs more power than our eye is designed to handle, and exposing our eye to that kind of power can damage the retina. And in a nutshell, solar eclipses are dangerous because the sun can come out from behind the moon and "surprise you" before you have a chance to look away. And this is actually even worse than when you normally look away from the sun because during the total eclipse, it is dark out, and your pupil therefore dialates so that it can let in enough light to get a good picture. Then, when the sun reappears and starts flooding the area with really bright light, not only are you staring straight at it, but your eye is in a state where it is wide open, and actively trying to let in as much light as possible.
This explains why it is easy to damage your eye when watching a total solar eclipse, and why you should either be sure to time it very carefully (and allow for a good margin of error), or just view the thing through one of those sets of cheap "dark" glasses they sell for the express purpose of looking at the sun without getting hurt.
Answered by: Gregory Ogin, Physics Undergraduate Student, UST, St. Paul, MN