Looking straight at the sun during a solar eclipse is more dangerous than staring at the sun on a bright sunny day because during the total eclipse period, your pupils will dilate, and the light can seriously harm your eyes. Then, when the sun comes back into full force, the area is deluged with light, and your eyes are more vulnerable because they are wide open and susceptible to damage.
There is only one way to look at the sun during an eclipse safely, and it is through special-purpose solar filters. These solar filters are employed in what are called "eclipse glasses." It is imperative to remember that typical sunglasses, even very dark ones, are not protective enough.