Well I didn't know the answer to your question, so I did a bit of research on the web, and learned something myself! It turns out that there are two kinds of sunscreen ingredients - chemical and physical.

The chemical ingredients work by absorbing the sun's UV rays. These are organic molecules which are able to absorb light in the appropriate frequency range. It's not really a chemical reaction - the molecules are excited into a higher energy state, which they then relax from gradually without re-emitting the dangerous UV radiation that would damage your skin.

The physical type simply work by covering your skin and blocking the radiation (much like wearing a shirt works!) These are oxides, including TiO₂ and ZnO. Incidentally, TiO₂ is also used in paints for the same reason - it is very good at scattering light. Here are some good web-sites that have some more information: sunscreens