Because ultraviolet light that causes skin cancer, sunburns and premature aging of the skin can still penetrate through clouds.
The UVB rays of light (think B for burn) are most affected by the weather. They are reduced in overcast days and in the winter. They are shorter and are filtered by glass. This is the light the SPF number on sunscreen refers to. It is most reduced, but not completely reduced on cloudy days.
UVA light however (think A for aging) is of a longer wavelength. It is not significantly changed in the winter or on a cloudy day. It can penetrate glass so it can get you when you are driving. Although it is less likely to cause immediate problems, such as a sunburn, it can accelerate aging of the skin and increase the risk of skin cancer.