High-energy ultraviolet light can damage unprotected eyes. Since our retinas are insensitive to pain, people looking directly at the sun wouldn't feel the destruction, and might not even notice it until hours later. Even worse is looking at the eclipse through unfiltered binoculars or a telescope, when retinal damage can take just a fraction of a second.
There are two basic ways of safely observing the eclipsed sun, indirectly or through filters.
The easiest indirect method is pinhole projection, in which you project the image of the sun through a small hole in a piece of card onto another sheet of white card. You can use binoculars mounted on a tripod (don't even think of looking through them!) to do the same thing, briefly - prolonged exposure can damage the optics because of the heat build-up.
For filtered direct viewing, sun-certified mylar glasses are cheap and do the job well, as does welder's glass #14. Silver-based black-and white film (fully exposed to light, developed to maximum density) also works. The Discovery Museum in Eureka and the gift shop at Prairie Creek Redwoods State Park are among those selling eclipse glasses. Do not look at the sun through: sunglasses, color film (which lacks silver), "space blanket" material or aluminized polyester gardening film.