If your eyes are exposed to excessive amounts of ultraviolet radiation over a short period of time, such as during the eclipse, you could experience photokeratitis, essentially a sunburn of the eye. Symptoms include red eyes, a foreign body sensation or gritty feeling in the eyes, extreme sensitivity to light and excessive tearing.
Unless you take proper precautions, looking directly at the sun during a partial eclipse can also cause solar retinopathy, which can result in permanent damage to your eyes. This is caused by light from the sun flooding the retina on the back of the eyeball. This exposure to solar radiation on the retina causes damage to its light-sensitive rod and cone cells by igniting a series of complex chemical reactions within the cells.