Radiation is simply light, and as light it carries energy, and as energy it can carry heat. You get hit with a powerful laser as in a sci- fi, and this is how it would kill you, by cooking you. However, solar radiation can include high frequency light, like ultraviolet, which is energetic enough to ionize atoms, which causes additional kinds of damage.

Ionizing radiation can do two things: first, it can simply kill cells, and it can cause mutations. Some mutations in body cells are bad, because they can break the controls that prevent cells from dividing, which results in them becoming cancerous. Sunburn is what you experience from dead cells that have been killed by ionizing radiation.