Modernism - an optimistic belief in human progress through science and reason - postmodernism - a loss of that belief - beware of oversimplifications

                                     Despite being posted by the 'gospel coalition' this is a reasonable attempt to explain the concepts. However, one might add that the optimism of modernism was partly a belief that reason, science, technology, education and democracy would create a better world. From Darwin to Freud, Marx to Joyce there is a belief in the power of the mind to understand, to make sense of the world.
Joyce wrote in "Portrait of the Artist as a Young Man", "By thinking of things you could understand them."
Some of that optimism survived World War 1.
However, World War 2, the mass murders in Auschwitz, the aerial bombings by the Nazis and the Allies, Hiroshima, Nagasaki all led to the emergence of Postmodernism - there is little optimism or faith in Camus and Beckett. 
However, there is at least a dogged determination to endure, to survive, to persist - as in Beckett's novel, "The Unnamable"

 "You must go on, I can't go on, I'll go on,"

However, Eliot's "The Waste Land"  1922, is a modernist classic with perhaps a foreshadowing of postmodern pessimism.
http://modernism.research.yale.edu/wiki/index.php/The_Waste_Land