Partial solar eclipses are very dangerous to the naked eyes. The reason behind this is the sun outputs more infrared radiation(heat), Ultraviolet radiation then our eyes can physically handle. And if you expose eyes to such powerful rays, this can permanently damage your retina.
This may surprise you but full solar eclipses are less dangerous then partial solar eclipses. In a partial eclipse there is two-part we see one is a black part and the other is the bright sun. When we try to see this our eyes try to focus upon both. In the process the sensitive neural tissues of your eyes damage. This damage is permanent, not recoverable with time or medicine.