Material chemistry is the study of materials. For example, you have polymers, ceramics, metals and semiconductors. Material chemists study these materials and figure out new ways to utilize their physical and chemical properties. It is related to our society b/c we have new products coming out everyday. Especially in the field of electronics. Nanotechnology is also hitting the market big. Researchers are constantly researching materials on the nano level. The reason being is that the nano level is the upper threshold where we see bulk material have different physical and chemical properties. They study the properties of different materials and try to combine them to make "composite" materials which would have the best characteristics of those combined.
Ex: carbon fibers (light and strong) with resin (strong and brittle) Can be combined and formed into jet airplane parts, race car bodies.