Light is an electromagnetic wave (google for that and you'll find some good stuff).
It interacts with matter because the electrons on the outside of atoms are electrically charged so are affected by changes in the electrical and magnetic fields around them (sort of the way that an object floating in water moves up and down when a wave comes by).
Generally if the light is absorbed by the matter (instead of being reflected, as with a mirror, or passing through unaffected, as with glass or clear air) the energy of the wave will end up as heat.