From https://en.wikipedia.org/wiki/Sunburn:

"It is the body's reaction to direct DNA damage from UVB light. This damage is mainly the formation of a thymine dimer. The damage is recognized by the body, which then triggers several defense mechanisms, including DNA repair to revert the damage, apoptosis and peeling to remove irreparably damaged skin cells, and increased melanin production to prevent future damage.

Melanin readily absorbs UV wavelength light, acting as a photoprotectant. By preventing UV photons from disrupting chemical bonds, melanin inhibits both the direct alteration of DNA, as well as the generation of free radicals, to prevent them from indirectly damaging DNA."

So... too much UV = DNA damage, sunscreen absorbs UV so it can't reach your skin.

My takeaway is: use sunscreen if you don't want literal radiation burns.