"Modernism" is that idea that humans are really great and smart and we are just getting greater and smarter. Humans have created Technology and Science which will allow is to do nearly anything and know nearly everything.
"Postmodernism" is the critique of modernism. It is any work or art that challenges those sentiments. Most simply put, postmodernism is the "critique of human rationality." That is a Philosophy definition, but it applies to it all. For example, in Architecture postmodernism is mixing styles from different periods and cultures which, according to our rational concepts, should not work together... but (hopefully) they do. Postmodern work challenges your rationality and the structures of how art and style should be.
